Work

Construction, extension and paths of near-homogeneous tournaments

Year: 2026

Type: article

Abstract: A homogeneous tournament is a tournament with 4 t + 3 vertices such that every arc is contained in exactly t + 1 cycles of length 3. Homogeneous tournaments are the first class of tournaments that are proved to be path extendable, which means that every nonhamiltonian path P in such a tournament T can be extended to a path P ′ with the same initial and terminal vertex and V ( P ′ ) = V ( P ) ∪ { u } for a certain vertex u ∈ V ( T ) ∖ V ( P ) . In order to find more path extendable tournaments we study the generalization of homogeneous tournaments called near-homogeneous tournaments, in which every arc is contained in t or t + 1 cycles of length 3. Near-homogeneity has been defined in tournaments with 4 t + 1 vertices. In this paper, we raise a new method to construct near-homogeneous tournaments with 4 t + 1 vertices. We then show that the definition of near-homogeneous tournament can be extended to tournaments with an even number of vertices. Finally we verify path extendability of near-homogeneous tournaments, thus expand the class of path extendable tournaments.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2025.12.059

Authors: Rongxia Tang, Zhaojun Chen, Zan-Bo Zhang

Institutions: Sun Yat-sen University, California Institute of Technology, Guangdong University Of Finances and Economics, Guangdong University of Finance

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Key Technologies Research and Development Program