Clique immersions in graphs of independence number two with certain forbidden subgraphs

Fecha

2021

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Elsevier

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item.page.issne

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Instituto de Ingenieria Matematica

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Resumen

The Lescure–Meyniel conjecture is the analogue of Hadwiger’s conjecture for the immersion order. It states that every graph contains the complete graph as an immersion, and like its minor-order counterpart it is open even for graphs with independence number 2. We show that every graph with independence number and no hole of length between 4 and satisfies this conjecture. In particular, every -free graph with satisfies the Lescure–Meyniel conjecture. We give another generalisation of this corollary, as follows. Let and be graphs with independence number at most 2, such that . If is -free, then satisfies the Lescure–Meyniel conjecture.

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Palabras clave

GRAPH IMMERSION, INDEPENDENCE NUMBER, FORBIDDEN SUBGRAPHS, CHROMATIC NUMBER, HADWIGER’S CONJECTURE, CLIQUE

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