Hajós Theorem For Colorings Of Edge-Weighted Graphs

Hajós theorem states that every graph with chromatic number at least k can be obtained from the complete graph K k by a sequence of simple operations such that every intermediate graph also has chromatic number at least k. Here, Hajós theorem is extended in three slightly different ways to colorings and circular colorings of edge-weighted graphs. These extensions shed some new light on the Hajós theorem and show that colorings of edge-weighted graphs are most natural extension of usual graph colorings.

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Correspondence to Bojan Mohar*.

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* Supported in part by the Ministry of Education, Science and Sport of Slovenia, Research Program P0–0507–0101.

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Mohar*, B. Hajós Theorem For Colorings Of Edge-Weighted Graphs. Combinatorica 25, 65–76 (2004). https://doi.org/10.1007/s00493-005-0005-7

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Mathematics Subject Classification (2000):

  • 05C15