منابع مشابه
The generalized acyclic edge chromatic number of random regular graphs
The r-acyclic edge chromatic number of a graph is defined to be the minimum number of colours required to produce an edge colouring of the graph such that adjacent edges receive different colours and every cycle C has at least min(|C|, r) colours. We show that (r − 2)d is asymptotically almost surely (a.a.s.) an upper bound on the r-acyclic edge chromatic number of a random d-regular graph, for...
متن کاملThe generalised acyclic edge chromatic number of random regular graphs
The r-acyclic edge chromatic number of a graph is defined to be the minimum number of colours required to produce an edge colouring of the graph such that adjacent edges receive different colours and every cycle C has at least min(|C|, r) colours. We show that (r − 2)d is asymptotically almost surely (a.a.s.) an upper bound on the r-acyclic edge chromatic number of a random d-regular graph, for...
متن کاملThe Chromatic Number of Random Regular Graphs
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
متن کاملEdge-face chromatic number and edge chromatic number of simple plane graphs
Given a simple plane graph G, an edge-face k-coloring of G is a function : E(G) [ F (G) ! f1, . . . ,kg such that, for any two adjacent or incident elements a, b 2 E(G) [ F (G), (a) 61⁄4 (b). Let e(G), ef(G), and (G) denote the edge chromatic number, the edge-face chromatic number, and the maximum degree of G, respectively. In this paper, we prove that ef(G) 1⁄4 e(G) 1⁄4 (G) for any 2-connected...
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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90182-1