Maximum vertex and face degree of oblique graphs
نویسندگان
چکیده
منابع مشابه
Dually vertex-oblique graphs
A vertex with neighbours of degrees d1 ≥ · · · ≥ dr has vertex type (d1, . . . , dr). A graph is vertex-oblique if each vertex has a distinct vertex-type. While no graph can have distinct degrees, Schreyer, Walther and Mel’nikov [Vertex oblique graphs, same proceedings] have constructed infinite classes of super vertex-oblique graphs, where the degree-types of G are distinct even from the degre...
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Let x be a vertex of a simple graph G. The vertex-type of x is the lexicographically ordered degree sequence of its neighbors. We call the graph G vertex-oblique if there are no two vertices in V (G) which are of the same vertex-type. We will show that the set of vertex-oblique graphs of arbitrary connectivity is infinite. © 2006 Elsevier B.V. All rights reserved.
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The acyclic chromatic number of a graph G, denoted a(G), is the minimum number of colors required to properly color the vertices of a graph such that there are no bichromatic cycles. The concept of acyclic coloring of a graph was introduced by [5] and is further studied in the last two decades in several works. Kostochka [6] proves that determining it is an NP-complete problem. Given the comput...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.05.023