Independence number and packing coloring of generalized Mycielski graphs
نویسندگان
چکیده
منابع مشابه
On Open Packing Number of Graphs
In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.
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For a graph G, let M(G) denote the Mycielski graph of G. The t-th iterated Mycielski graph of G, M(G), is defined recursively by M0(G) = G and M(G)= M(Mt−1(G)) for t ≥ 1. Let χc(G) denote the circular chromatic number of G. We prove two main results: 1) Assume G has a universal vertex x, then χc(M(G)) = χ(M(G)) if χc(G − x) > χ(G − x) − 1/2 and G is not a star, otherwise χc(M(G)) = χ(M(G)) − 1/...
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Let G be a graph with no three independent vertices. How many edges of G can be packed with edge-disjoint copies of Kk? More specifically, let fk(n,m) be the largest integer t such that for any graph with n vertices, m edges, and independence number 2, at least t edges can be packed with edge-disjoint copies ofKk. Turán’s Theorem together with Wilson’s Theorem assert that fk(n,m) = (1−o(1)) 2 4...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2337