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Journal Articles SIAM Journal on Discrete Mathematics Year : 2023

Strengthening a theorem of Meyniel

Abstract

For an integer k ≥ 1 and a graph G, let K k (G) be the graph that has vertex set all proper k-colorings of G, and an edge between two vertices α and β whenever the coloring β can be obtained from α by a single Kempe change. A theorem of Meyniel from 1978 states that K 5 (G) is connected with diameter O(5 |V (G)|) for every planar graph G. We significantly strengthen this result, by showing that there is a positive constant c such that K 5 (G) has diameter O(|V (G)| c) for every planar graph G.
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hal-04156967 , version 1 (10-07-2023)

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Quentin Deschamps, Carl Feghali, František Kardoš, Clément Legrand-Duchesne, Théo Pierron. Strengthening a theorem of Meyniel. SIAM Journal on Discrete Mathematics, 2023, 37 (2), ⟨10.1137/22M1474394⟩. ⟨hal-04156967⟩
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