A characterization of rich c-partite (c > 7) tournaments without (c + 2)-cycles

Jie Zhang; Zhilan Wang; Jin Yan

doi:10.46298/dmtcs.9732

Jie Zhang ; Zhilan Wang ; Jin Yan - A characterization of rich c-partite (c > 7) tournaments without (c + 2)-cycles

dmtcs:9732 - Discrete Mathematics & Theoretical Computer Science, December 5, 2023, vol. 25:2 - https://doi.org/10.46298/dmtcs.9732

A characterization of rich c-partite (c > 7) tournaments without (c + 2)-cyclesArticle

Authors: Jie Zhang ; Zhilan Wang ; Jin Yan

Let c be an integer. A c-partite tournament is an orientation of a complete c-partite graph. A c-partite tournament is rich if it is strong, and each partite set has at least two vertices. In 1996, Guo and Volkmann characterized the structure of all rich c-partite tournaments without (c + 1)-cycles, which solved a problem by Bondy. They also put forward a problem that what the structure of rich c-partite tournaments without (c + k)-cycles for some k>1 is.
In this paper, we answer the question of Guo and Volkmann for k = 2.

https://doi.org/10.46298/dmtcs.9732

Source: arXiv.org:2206.10823

Volume: vol. 25:2

Section: Graph Theory

Published on: December 5, 2023

Accepted on: September 24, 2023

Submitted on: June 23, 2022

Keywords: Mathematics - Combinatorics

Licence: arXiv.org - Non-exclusive license to distribute