Line game-perfect graphs
Stephan Dominique Andres, Wai Lam Fong

TL;DR
This paper characterizes line game-perfect graphs for various edge colouring game variants, providing forbidden subgraph characterizations and structural descriptions for each case.
Contribution
It introduces a comprehensive characterization of line $[X,Y]$-perfect graphs through forbidden subgraphs and structural descriptions for all six game variants.
Findings
Characterization of line $[X,Y]$-perfect graphs for all variants.
Forbidden subgraph descriptions for each case.
Explicit structural descriptions for each case.
Abstract
The -edge colouring game is played with a set of colours on a graph with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player has the first move. . If , then only player may skip any move, otherwise skipping is not allowed for any player. A move consists of colouring an uncoloured edge with one of the colours such that adjacent edges have distinct colours. When no more moves are possible, the game ends. If every edge is coloured in the end, Alice wins; otherwise, Bob wins. The -game chromatic index is the smallest nonnegative integer such that Alice has a winning strategy for the -edge colouring game played on with colours. The graph is called line -perfect if, for any edge-induced subgraph of ,…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems
