Total Game Coloring of Graphs

TL;DR

This paper investigates the total game coloring problem in graphs, determining exact total game chromatic numbers for specific graph classes and analyzing strategies for winning, while exploring relationships with other coloring parameters.

Contribution

It provides exact values for total game chromatic numbers of certain graphs and establishes strategies and relations with other coloring indices.

Findings

Exact total game chromatic numbers for some graph classes

Strategies for the first player's winning approach

Relation between total game coloring number and game coloring index

Abstract

Total variant of well known graph coloring game is considered. We determine exact values of total game chromatic number for some classes of graphs and show show the strategie for first player to win the game. We also show relation between total game coloring number and game coloring index.