2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10

Journal of Combinatorial Optimization - Given a graph G and a list assignment L(v) for each vertex of v of G, a proper L-list-coloring of G is a function that maps every vertex to a color in L(v)...     

Some results on the injective chromatic number of?graphs

A k-coloring of a graph G=(V,E) is a mapping c:V??{1,2,??,k}. The coloring c is injective if, for every vertex v??V, all the neighbors of v are assigned with distinct colors. The injective chromatic number ?? _i (G) of G is the smallest k such that G has an injective k-coloring. In this paper, we prove that every K ₄-minor free graph G with maximum degree ????1 has $\chi_{i}(G)\le \lceil \frac{3}{2}\Delta\rceil$ . Moreover, some related results and open problems are given.     

A sufficient condition for planar graphs with girth 5 to be (1, 7)-colorable

A graph G is \((d_1, d_2)\)-colorable if its vertices can be partitioned into subsets \(V_1\) and \(V_2\) such that in \(G[V_1]\) every vertex has degree at most \(d_1\) and in \(G[V_2]\) every vertex has degree at most \(d_2\). Let \(\mathcal {G}_5\) denote the family of planar graphs with minimum cycle length at least 5. It is known that every graph in \(\mathcal {G}_5\) is \((d_1, d_2)\)-colorable, where \((d_1, d_2)\in \{(2,6), (3,5),(4,4)\}\). We still do not know even if there is a finite positive d such that every graph in \(\mathcal {G}_5\) is (1, d)-colorable. In this paper, we prove that every graph in \(\mathcal {G}_5\) without adjacent 5-cycles is (1, 7)-colorable. This is a partial positive answer to a problem proposed by Choi and Raspaud that is every graph in \(\mathcal {G}_5\;(1, 7)\)-colorable?.     

On the adjacent vertex-distinguishing total chromatic numbers of the graphs with Δ (G) = 3

Let be a simple graph and T(G) be the set of vertices and edges of G. Let C be a k-color set. A (proper) total k-coloring f of G is a function such that no adjacent or incident elements of T(G) receive the same color. For any , denote . The total k-coloring f of G is called the adjacent vertex-distinguishing if for any edge . And the smallest number of colors is called the adjacent vertex-distinguishing total chromatic number of G. In this paper, we prove that for all connected graphs with maximum degree three. This is a step towards a conjecture on the adjacent vertex-distinguishing total coloring. MSC: 05C15     

Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ

An adjacent vertex-distinguishing edge coloring, or avd-coloring, of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let $\operatorname {mad}(G)$ and Δ(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every graph G with Δ(G)≥5 and $\operatorname{mad}(G) < 3-\frac {2}{\Delta}$ can be avd-colored with Δ(G)+1 colors. This completes a result of Wang and Wang (J. Comb. Optim. 19:471–485, 2010).     

Vertices in all minimum paired-dominating sets of?block graphs

Let G=(V,E) be a simple graph without isolated vertices. A set S?V is a paired-dominating set if every vertex in V?S has at least one neighbor in S and the subgraph induced by S contains a perfect matching. In this paper, we present a linear-time algorithm to determine whether a given vertex in a block graph is contained in all its minimum paired-dominating sets.     

Is there any polynomial upper bound for the universal labeling of graphs?

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem.     

The competition number of a graph with?exactly?two?holes

Given an acyclic digraph D, the competition graph C(D) of D is the graph with the same vertex set as D and two distinct vertices x and y are adjacent in C(D) if and only if there is a vertex v in D such that (x,v) and (y,v) are arcs of D. The competition number κ(G) of a graph G is the least number of isolated vertices that must be added to G to form a competition graph. The purpose of this paper is to prove that the competition number of a graph with exactly two holes is at most three.     

Long cycles in hypercubes with optimal number of?faulty vertices

Let f(n) be the maximum integer such that for every set F of at most f(n) vertices of the hypercube Q _n , there exists a cycle of length at least 2 ⁿ ?2|F| in Q _n ?F. Casta?eda and Gotchev conjectured that $f(n)=\binom{n}{2}-2$ . We prove this conjecture. We also prove that for every set F of at most (n ²+n?4)/4 vertices of Q _n , there exists a path of length at least 2 ⁿ ?2|F|?2 in Q _n ?F between any two vertices such that each of them has at most 3 neighbors in F. We introduce a new technique of potentials which could be of independent interest.     

Control at work: a generalized resource factor for the prevention of musculoskeletal symptoms?

During the last two decades two potent groups of predictors for work-related musculoskeletal problems have been identified: physical work load and poor psychosocial working conditions. However, little is known about their combined effects. In this study the buffering effect of control at work with respect to the negative effects of psychological demands and physical work load on musculoskeletal problems is examined. All study variables were sampled from 431 people working in geriatric nursing homes in Germany by means of questionnaires. Main effects and interactions were tested with multiple regression analysis. The results showed that control buffered the effects of high psychological demands, but not of high physical work load; the buffering effect of control was observed only when physical work load was low. The combined effects of demands and physical work load were over-additive. Thus, the power of different predictors for musculoskeletal symptoms depended on the level of other predictors. This suggests that the efficiency of certain strategies for the prevention of musculoskeletal problems is likely to depend on the level of risk factors, with different strategies being appropriate for different levels of risk.     

Overconfidence at work: Does overconfidence survive the checks and balances of organizational life?

This review considers the role of overconfidence in organizational life, focusing on ways in which individual-level overconfidence manifests in organizations. The research reviewed offers a pessimistic assessment of the efficacy of either debiasing tools or organizational correctives, and identifies some important ways in which organizational dynamics are likely to exacerbate overconfidence among individuals. The organizational consequences of overconfidence can be substantial, especially when it comes from those at the top of the organization. However, there are also reasons to suspect that the research literature exaggerates the prevalence of overconfidence.     

Blazing new trails or opportunity lost? Evaluating research at the intersection of leadership and entrepreneurship

More than a decade ago, scholars formally conceptualized the potential synergy between leadership and entrepreneurship scholarship. Our work highlights research accomplishments occurring at the interface of these two intellectual areas as well as identifying untapped possibilities for continued research. We highlight how recent efforts have witnessed a mutual exchange of ideas that present opportunities benefiting both fields. Drawing from four key domains of entrepreneurship previously proposed to mutually inform future leadership research efforts, we make suggestions for integrating entrepreneurial opportunities, the roles of individual and entrepreneurial teams, the modes of organizing entrepreneurial ventures, and differing entrepreneurial environments with key trends important to leadership research, such as servant leadership and leader-member exchange theory. Overall, our work provides an assessment of the state of the art surrounding the coalescence of leadership and entrepreneurship research and sets an agenda for the next decade of research at this intersection.     

Supported,detached, or marginalized? The ambivalent role of social capital on stress at work

Relationships with work colleagues can mitigate job stress; this article proposes a new perspective on such effects, in accordance with social capital theory, to delineate the potentially distinct impacts of the two dimensions of relational and structural social capital. A partial least squares analysis of network data in a medium-sized company (N = 343) offers evidence of an effect of the relational dimension (tie strength), through social support. The structural dimension (bridging ties, i.e. whether an employee has social ties with members of other departments) reveals a dual effect involving reduced stress but also diminished social support, which can increase stress. These dual effects reflect the two levels on which bridging ties act, namely, cognitive (selfdistancing) and social (marginalization from the immediate work context) levels. Next, with two scenario-based experiments (N = 289 and 245), the authors manipulate bridging ties and gain further evidence of the proposed mechanisms. These findings highlight the social underpinnings of stress and the critical role of the structure, not just the quality, of work relationships. They also identify a dark side of bridging ties, which can enhance individual performance but also create the potential for negative wellbeing outcomes.     

2. Is it lonely at the top?: The independence and interdependence of power holders

Although power is considered by many to be a fundamental way people organize social relationships, we know little about the psychological experience of being powerful, or the underlying mechanisms through which power affects individuals. In this paper, we review evidence suggesting that power creates a subjective sense of separation and distinctiveness from others, such that high power individuals have more independent self construals than low power individuals. We also review research demonstrating that power is related to the quantity of interconnections with others, such that high power individuals have more interdependent relational structures than low power individuals. We argue that independent self construals and interdependent relational structures occur simultaneously, and mutually reinforce one another. We review current research that acknowledges both dimensions of power, and propose specific mechanisms that underlie the relationship between independent self construal and interdependent relational structures.     

Seeds of Corruption? The Contingent Role of Ties to Politicians and Foreign Subsidiary Relations with Government-Sponsored Financial Institutions

In drawing from transaction cost economics and social network theories, this study examines the influence of corruption as a determinant of foreign subsidiary formal contracting practices with government-sponsored financial institutions. We hypothesize that lower corruption distance (between parent home and host countries) and higher perceived corruption (in host country) are positively related, and mutually reinforcing, when considering a foreign subsidiary's propensity to formally contract with government-sponsored financial institutions. We also suggest that these relationships strengthen with the intensification of political ties to government officials who can offer preferential political services via contractual agreements, changing the nature of market transactions in favour of a foreign subsidiary. We found support for our hypotheses using data from a sample of over 350 subsidiaries located in the Philippines and Thailand.     

Rumination for innovation? Analysing the longitudinal effects of work-related rumination on creativity at work and off-job recovery

Work-related rumination is not a single construct, but consists of a dimension associated with negative emotions or affect (affective rumination), and a dimension associated with reflective thinking and applying strategies to solve problems (problem-solving pondering). In this three-wave longitudinal study across two years (N?=?630) we investigated whether the relationships between work-related rumination, off-job recovery, and creativity at work varied along the two dimensions of work-related rumination. In addition, we tested whether the relationships followed normal, reversed, or reciprocal causation. The results showed, first, that in a one-year perspective affective rumination, but not problem-solving pondering, was negatively related to off-job recovery and that problem-solving pondering, but not affective rumination, was positively related to creativity at work. Second, in a two-year perspective, reversed effects were detected as creativity at work was negatively related to affective rumination and positively to off-job recovery. Our results suggest that the quality of work-related thoughts determines whether the outcome is beneficial or detrimental. Occupational health interventions that only advise employees to stop thinking about work during off-job time, may therefore be too simplistic.     

A new approach to analyzing the Achilles' heel of multisource feedback programs: Can we really trust ratings of leaders at the group level of analysis?

This research addresses the Achilles’ heel of all multi-source leadership feedback programs regardless of whether they use 360°, 270°, or 180° ratings. Namely, should all feedback be universally aggregated by feedback groups and reported to respondents? A sample of raters from the Center for Creative Leadership (N = 15,500 including subordinates, peers, and others) was grouped to align with each raters’ matching focal subject (J = 1,550). Two scales from CCL’s Benchmarks instrument (Building and Mending Relationships and Career Management) were used to: (1) predict a derailment factor (Problems with Interpersonal Relationships) and (2) determine the operative level of analysis and its aggregation characteristics using Within and Between Analysis (WABA). In many cases, the variables under consideration did not aggregate optimally. Using a technique based upon each group’s coefficient of variation as a measure of internal consensus, between 3% and 25% of groups should not have their averages reported. Alternative approaches are discussed.     

The Timing of Capacity Investment with Lead Times: When Do Firms Act in Unison?

We study competitive capacity investment for the emergence of a new market. Firms may invest either in capacity leading demand or in capacity lagging demand at different costs. We show how the lead time and other operational factors including volume flexibility, existing capacity, and demand uncertainty impact equilibrium outcomes. Our results indicate that a type of bandwagon behavior is the most likely equilibrium outcome: if both firms are going to invest, then they are most likely to act in unison. Contrary to much received wisdom, we show that leader–follower behavior is very uncommon in equilibrium where firms do not have volume flexibility, and will not occur at all if lead times are sufficiently short. On the other hand, if there is volume flexibility in production, then the likelihood of this sequential investment behavior increases. Our findings underscore the importance of operational characteristics in determining the competitive dynamics of capacity investment timing.     

Birds of a feather?: Firm sales growth and narcissism in the upper echelons at the CEO-TMT interface

Blending conceptual framing from the CEO-TMT interface literature with upper echelons decision-making theory, we develop a model of the role of CEO narcissism and narcissism in the upper echelons. We argue that narcissistic CEOs tend to have higher narcissism in their Top Management Teams (N-TMTs). In turn, TMTs characterized by narcissism can benefit from positive aspects of narcissism while avoiding its pitfalls; especially when strategic decision speed is slower and behavioral integration is higher. In a field study of 104 TMTs from publicly-listed South Korean firms, we find an association between narcissistic CEOs and N-TMT, and that N-TMT mediates in the indirect, conditional relationship between CEO narcissism and sales growth. We also invoke threshold theory in anticipation that outcomes associated with N-TMT may be nonlinear. In support of our threshold hypothesis, we find a curvilinear relationship between N-TMT and sales growth; and this curvilinear relationship is stronger for a small number of TMTs scoring high on N-TMT (> +2SD), where TMTs’ activities are defined by deliberative integration. The pattern of results we report provides evidence for the importance of accounting for narcissism in the upper echelons as a predictor of sales growth, and key contextual moderators of this relationship.