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In this paper we consider undirected graphs and hypergraphs. We denote by V (G) the vertex set of a graph G and the edge set by E(G). Notations v(G) and e(G) in our paper stand for the number of vertices and edges respectively. We denote by dG(v) the degree of vertex v ∈ V (G) in G. We denote

Abstract. We characterize edge-colored graphs in which every edge belongs to some properly colored cycle. We obtain our result by applying a characterization of 1-extendable graphs. Key words. Edge-colored graphs, properly colored cycles, 1-extendable graphs, cycle covers. 1. Introduction, notation

give a complete description of all proper colorings, all feasible partitions, chromatic polynomial and chromatic spectrum of every colorable BST S(15).

An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C0

klazar at kam.mff.cuni.cz Using a counting argument called Turán sieve (with motivation in number theory), Liu and Murty proved in [3, Theorem 4] an inequality on the number of proper vertex colorings, by λ colors, of a simple graph G = (V, E) with v = |V | vertices and e = |E | edges: #(proper λ-colorings

Let Kcn denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kcn) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kcn is a cycle (path) in which adjacent edges have distinct colors. B

We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every m-good edge-coloring of K n yields a properly edge-colored

It is shown that for every ɛ> 0 and n> n0(ɛ), any complete graph K on n vertices whose edges are colored so that no vertex is incident with more than (1 − 1 √ 2 − ɛ)n edges of the same color, contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between

The goal of this work is to accurately detect and localize boundaries in natural scenes using local image measurements. We formulate features that respond to characteristic changes in brightness, color, and texture associated with natural boundaries. In order to combine the information from