On indicated coloring of some classes of graphs
P. Francis, S. Francis Raj, M. Gokulnath

TL;DR
This paper studies indicated coloring in specific classes of graphs, providing structural characterizations and proving that these classes are k-indicated colorable for all k greater than or equal to their chromatic number.
Contribution
It offers new structural insights and proves k-indicated colorability for certain classes of graphs with forbidden induced subgraphs.
Findings
Structural characterization of certain {P5,K4,Kite,Bull}-free graphs with induced C5.
Proof that specific graph classes are k-indicated colorable for all k ≥ χ(G).
Partial answer to a question by A. Grzesik on indicated coloring.
Abstract
Indicated coloring is a type of game coloring in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly, using a fixed set of colors. The goal of Ann is to achieve a proper coloring of the whole graph, while Ben is trying to prevent the realization of this project. The smallest number of colors necessary for Ann to win the game on a graph (regardless of Ben's strategy) is called the indicated chromatic number of , denoted by . In this paper, we obtain structural characterization of connected -free graphs which contains an induced and connected -free graphs that contains an induced . Also, we prove that -free graphs that contains an induced and…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
