Supermodular Extension of Vizing's EdgeColoring Theorem
Abstract
Kőnig's edgecoloring theorem for bipartite graphs and Vizing's edgecoloring theorem for general graphs are celebrated results in graph theory and combinatorial optimization. Schrijver generalized Kőnig's theorem to a framework defined with a pair of intersecting supermodular functions. The result is called the supermodular coloring theorem. This paper presents a common generalization of Vizing's theorem and a weaker version of the supermodular coloring theorem. To describe this theorem, we introduce strongly tripleintersecting supermodular functions, which are extensions of intersecting supermodular functions. The paper also provides an alternative proof of Gupta's edgecoloring theorem using a special case of this supermodular version of Vizing's theorem.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.07150
 arXiv:
 arXiv:2211.07150
 Bibcode:
 2022arXiv221107150M
 Keywords:

 Mathematics  Combinatorics