Split and balanced colorings of complete graphs
نویسندگان
چکیده
منابع مشابه
Split and balanced colorings of complete graphs
An (r, n)-split coloring of a complete graph is an edge coloring with r colors under which the vertex set is partitionable into r parts so that for each i, part i does not contain K, in color i. This generalizes the notion of split graphs which correspond to (2, 2)-split colorings. The smallest N for which the complete graph Ks has a coloring which is not (r,n)-split is denoted by f,.(n). Balan...
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A graph G is called a complete k-partite (k ≥ 2) graph if its vertices can be partitioned into k independent sets V1, . . . , Vk such that each vertex in Vi is adjacent to all the other vertices in Vj for 1 ≤ i < j ≤ k. A complete k-partite graph G is a complete balanced kpartite graph if |V1| = |V2| = · · · = |Vk|. An edge-coloring of a graph G with colors 1, . . . , t is an interval t-colorin...
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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...
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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: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00323-9