Counting Gallai 3-colorings of complete graphs
نویسندگان
چکیده
منابع مشابه
Gallai colorings of non-complete graphs
Gallai-colorings of complete graphs – edge colorings such that no triangle is colored with three distinct colors – occur in various contexts such as the theory of partially ordered sets (in Gallai’s original paper), information theory and the theory of perfect graphs. We extend here Gallai-colorings to non-complete graphs and study the analogue of a basic result – any Gallai-colored complete gr...
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The Gallai graph and the anti-Gallai graph of a graph G have the edges of G as their vertices. Two edges of G are adjacent in the Gallai graph of G if they are incident but do not span a triangle in G; they are adjacent in the anti-Gallai graph of G if they span a triangle in G. In this paper we show: The Four Color Theorem can be equivalently stated in terms of anti-Gallai graphs; the problems...
متن کاملGallai and anti-Gallai graphs
This chapter deals with two graph classes the Gallai graphs and the anti-Gallai graphs. \Ve construct infinitely many pairs of graphs G and H such that f( G) = r( H). The existence of a finite family offorbidden subgraphs for the Gallai graphs and the ant.i-Gallai graphs to be H-frce, for any fillit.e graph H is proved and the forbidden subgraph characterizations of G for which the Gallai graph...
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An edge-coloring of a graph G with colors 1, 2, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, W (G) denotes the greatest value of t for which G has an int...
متن کاملSemi-algebraic colorings of complete graphs
In this paper, we consider edge colorings of the complete graph, where the vertices are points in R, and each color class Ei is defined by a semi-algebraic relation of constant complexity on the point set. One of our main results is a multicolor regularity lemma: For any 0 < ε < 1, the vertex set of any such edge colored complete graph with m colors can be equitably partitioned into at most (m/...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.05.015