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Article Dans Une Revue Journal of Combinatorial Theory, Series B Année : 2021

A Menger-like property of tree-cut width

Résumé

In 1990, Thomas proved that every graph admits a tree decomposition of minimum width that additionally satisfies a certain vertex-connectivity condition called leanness [A Menger-like property of tree-width: The finite case. Journal of Combinatorial Theory, Series B, 48(1):67-76, 1990]. This result had many uses and has been extended to several other decompositions. In this paper, we consider tree-cut decompositions, that have been introduced by Wollan as a possible edge-version of tree decompositions [The structure of graphs not admitting a fixed immersion. Journal of Combinatorial Theory, Series B, 110:47-66, 2015]. We show that every graph admits a tree-cut decomposition of minimum width that additionally satisfies an edge-connectivity condition analogous to Thomas' leanness.
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Dates et versions

hal-03094586 , version 1 (04-01-2021)

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Archontia C Giannopoulou, O-Joung Kwon, Jean-Florent Raymond, Dimitrios M. Thilikos. A Menger-like property of tree-cut width. Journal of Combinatorial Theory, Series B, 2021, 148, pp.1-22. ⟨10.1016/j.jctb.2020.12.005⟩. ⟨hal-03094586⟩
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