You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.
Speaker: Lale Özkahya Hacettepe University)
“Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length”
Abstract: The problem of finding the minimum number of colors to color a graph properly without containing any bicolored copy of a fixed family of subgraphs has been widely studied. Most well-known examples are star coloring and acyclic coloring of graphs (Grüunbaum, 1973) where bicolored copies of P4 and cycles are not allowed, respectively. We introduce a variation of these problems and study proper coloring of graphs not containing a bicolored path of a fixed length and provide general bounds for all graphs. A Pk-coloring of an undirected graph G is a proper vertex coloring of G such that there is no bicolored copy of Pk in G; and the minimum number of colors needed for a Pk-coloring of G is called the Pk-chromatic number of G; denoted by sk(G). We found bounds on s_k(G) for all graphs. Moreover, we find the exact values for the Pk-chromatic number of the products of some cycles and paths for k = 5; 6. This is joint work with Alaittin Kırtışoğlu.
Date: Thursday, March 24, 2022
Time: 18:00-19:00, GMT+3.
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