منابع مشابه
Colorings of the d-regular infinite tree
The existence of small d-regular graphs of a prescribed girth g is equivalent to the existence of certain codes in the d-regular infinite tree. We show that in the tree ‘‘perfect’’ codes exist, but those are usually not ‘‘graphic’’. We also give an explicit coloring that is ‘‘nearly perfect’’ as well as ‘‘nearly graphic’’. r 2004 Elsevier Inc. All rights reserved.
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It is calculated the number of symmetric r-colorings of vertices of a regular n-gon and the number of equivalence classes of symmetric r-colorings [1, 2]. A coloring is symmetric if it is invariant in respect to some mirror symmetry with an axis crossing center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.
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An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...
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In this paper we investigate colorings of sets avoiding similarly colored subsets. If S is an arbitrary colored set and T is a "xed family of bijections of S to itself, then two subsets A; B ⊆ S are said to be colored similarly with respect to T, if there exists a transformation t ∈T mapping A onto B, and preserving a coloring of A. This general setting covers some well-known topics such as non...
متن کاملInterference-Minimizing Colorings of Regular Graphs
Communications problems that involve frequency interference, such as the channel assignment problem in the design of cellular telephone networks, can be cast as graph coloring problems in which the frequencies (colors) assigned to an edge’s vertices interfere if they are too similar. The paper considers situations modeled by vertex-coloring d-regular graphs with n vertices using a color set {1,...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2004
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2003.11.004