منابع مشابه
Large Chromatic Number and Ramsey Graphs
Let Q(n, χ) denote the minimum clique size an n-vertex graph can have if its chromatic number is χ . Using Ramsey graphs we give an exact, albeit implicit, formula for the case χ ≥ (n + 3)/2.
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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...
متن کاملCircular Chromatic Ramsey Number
Let χc(H) denote the circular chromatic number of a graph H. For graphs F and G, the circular chromatic Ramsey number Rχc(F,G) is the infimum of χc(H) over graphs H such that every red/blue edge-coloring of H contains a red copy of F or a blue copy of G. We characterize Rχc(F,G) in terms of a Ramsey problem for the families of homomorphic images of F and G. Letting zk = 3 − 2 −k, we prove that ...
متن کاملGraphs with Large Distinguishing Chromatic Number
The distinguishing chromatic number χD(G) of a graph G is the minimum number of colours required to properly colour the vertices of G so that the only automorphism of G that preserves colours is the identity. For a graph G of order n, it is clear that 1 6 χD(G) 6 n, and it has been shown that χD(G) = n if and only if G is a complete multipartite graph. This paper characterizes the graphs G of o...
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In the first part of these notes we use a probabilistic method to show the existence of graphs with large girth and large chromatic number. In the second part we give an explicit example of such graphs. It is mostly based on the third chapter of Some Applications Of Modular Forms by Peter Sarnak and also the third and forth chapters of Elementary Number Theory, Group Theory, And Ramanujan Graph...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2012
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-012-1179-6