منابع مشابه
Graphs with large girth are b-continuous
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of G is the maximum integer b(G) for which G has a b-coloring with b(G) colors. A graph G is b-continuous if G has a b-coloring with k colors, for every integer k in the interval [χ(G), b(G)]. It is known that not all graphs ar...
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A proper vertex coloring of a graph G is equitable if the size of color classes differ by at most one. The equitable chromatic threshold of G, denoted by ∗Eq(G), is the smallest integer m such that G is equitably n-colorable for all n m. We prove that ∗Eq(G) = (G) if G is a non-bipartite planar graph with girth 26 and (G) 2 or G is a 2-connected outerplanar graph with girth 4. © 2007 Elsevier B...
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We show that a planar graph with girth at least 20t−2 3 has circular chromatic number at most 2+ 1t , improving earlier results. This follows from a general result establishing homomorphisms into special targets for graphs with given girth and given maximum average degree. Other applications concern oriented chromatic number and homomorphisms into mixed graphs with colored edges.
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We study the evolution of cooperation in populations where individuals play prisoner’s dilemma on a network. Every node of the network corresponds on an individual choosing whether to cooperate or defect in a repeated game. The players revise their actions by imitating those neighbors who have higher payoffs. We show that when the interactions take place on graphs with large girth, cooperation ...
متن کاملConstructions for Cubic Graphs with Large Girth
The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer μ0(g), the smallest number of vertices for which a cubic graph with girth at least g exists, and furthermore, the minimum value μ0(g) is attained by a graph whose girth is exactly g. The values of μ0(g) when 3 ≤ g ≤ 8 have been known for over thirty y...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2015
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498815501121