منابع مشابه
Disconnected Colors in Generalized Gallai-Colorings
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. A basic property of GallaiQ1 colorings with at least three colors is that at least one of the color classes must span a disconnected...
متن کاملGallai colorings and domination in multipartite digraphs
Assume that D is a digraph without cyclic triangles and its vertices are partitioned into classes A1, . . . , At of independent vertices. A set U = ∪i∈SAi is called a dominating set of size |S| if for any vertex v ∈ ∪i/ ∈SAi there is a w ∈ U such that (w, v) ∈ E(D). Let β(D) be the cardinality of the largest independent set of D whose vertices are from different partite classes of D. Our main r...
متن کاملGallai 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...
متن کاملRamsey-type results for Gallai colorings
A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following: 1. a monochromatic double star with at...
متن کاملInjective colorings of planar graphs with few colors
An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. In this paper some results on injective colorings of planar graphs with few colors are presented. We show that all planar graphs of girth ≥19 and maximum degree ∆ are injectively ∆-colorable. We also show that all planar graphs of girth ≥10 are injectively (...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2020
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2020.103087