An algorithm for the chromatic number of a graph
نویسندگان
چکیده
منابع مشابه
total dominator chromatic number of a graph
given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...
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We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality and discuss applications of the theorem. Keywords— Brooks’ Theorem, Group coloring, Group chromatic number.
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Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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For a nontrivial connected graph G, let c : V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6= NC(v) for every pair u, v of adjacent vertices of G. The minimum number of colors required of such a coloring is calle...
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In 1982, Zaslavsky introduced the concept of a proper vertex colouring of a signed graph G as a mapping φ : V (G) → Z such that for any two adjacent vertices u and v the colour φ(u) is different from the colour σ(uv)φ(v), where is σ(uv) is the sign of the edge uv. The substantial part of Zaslavsky’s research concentrated on polynomial invariants related to signed graph colourings rather than on...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1971
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/14.1.38