NDLI: On Indicated Chromatic Number of Graphs

Content Provider	Springer Nature Link
Author	Patil, H. P. Pandiya Raj, R. Francis Raj, S.
Copyright Year	2016
Abstract	Indicated coloring is a graph coloring game in which there are two players jointly coloring the vertices of a graph in such a way that both can see the entire graph at all the time and in each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly without creating a monochromatic edge, using a fixed set of colors. The aim of Ann is to achieve a proper coloring for G, while Ben is trying to create a situation where all the colors occur on vertices adjacent to some uncolored vertex. The smallest number of colors necessary for Ann to win the game on a graph G (regardless of Ben’s strategy) is called the indicated chromatic number of G, and is denoted by $$\chi _i(G)$$ . In this paper, we obtain some upper bounds for the indicated chromatic number of graphs and find a smallest 3-regular graph for which the indicated chromatic number is 4. In addition, we introduce the concept of criticality of graphs with respect to the indicated chromatic number. Also we show that $$\{P_5,K_4-e\}$$ -free graphs are k-indicated colorable for all $$k\ge \chi (G)$$ .
Ending Page	219
Page Count	17
Starting Page	203
File Format	PDF
ISSN	09110119
e-ISSN	14355914
Journal	Graphs and Combinatorics
Issue Number	1
Volume Number	33
Language	English
Publisher	Springer Japan
Publisher Date	2016-11-29
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Uniquely colorable graphs Indicated coloring Mycielski graphs Structural characterization of families of graphs Color critical graphs Engineering Design Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science

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