On the complexity of turning a graph into the analogue of a clique

Abstract : An orientation of an undirected graph G has weak diameter k if, for every pair {u, v} of vertices of G, there is a directed path with length at most k joining u and v in either direction. We show that deciding whether an undirected graph admits an orientation with weak diameter k is NP-complete for every k ≥ 2. This result implies the NP-completeness of deciding whether an undirected graph can be turned into the analogue of a clique for proper colouring of several augmented kinds of graphs.
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https://hal.archives-ouvertes.fr/hal-02417841
Contributor : Sergey Kirgizov <>
Submitted on : Wednesday, December 18, 2019 - 1:55:41 PM
Last modification on : Monday, January 13, 2020 - 1:18:26 AM

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  • HAL Id : hal-02417841, version 1

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Julien Bensmail, Romaric Duvignau, Sergey Kirgizov. On the complexity of turning a graph into the analogue of a clique. 9th International colloquium on graph theory and combinatorics (ICGT 2014), Jun 2014, Grenoble, France. ⟨hal-02417841⟩

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