Total chromatic sum for trees

Michał Małafiejski; Krzysztof Ocetkiewicz; Ewa Kubicka; Grzegorz Kubicki

Total chromatic sum for trees

Abstract

The total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.

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Category:: Conference activity
Type:: publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
Language:: English
Publication year:: 2021
Bibliographic description:: Małafiejski M., Ocetkiewicz K., Kubicka E., Kubicki G.: Total chromatic sum for trees// / : , 2021,
Verified by:: Gdańsk University of Technology