Isomorphism testing of $k$-spanning tournaments is Fixed Parameter Tractable

TL;DR

This paper proves that testing whether two arc-colored tournaments are isomorphic, under the condition of being $k$-spanning, can be efficiently solved using fixed-parameter tractability techniques.

Contribution

The paper establishes that isomorphism testing for $k$-spanning tournaments is fixed-parameter tractable, providing a new approach for this class of problems.

Findings

Isomorphism testing of $k$-spanning tournaments is fixed-parameter tractable.

The union of arc-color classes of bounded valency forms a strongly connected digraph.

The result advances understanding of structural graph isomorphism problems.

Abstract

An arc-colored tournament is said to be $k$-spanning for an integer $k\geq 1$ if the union of its arc-color classes of maximal valency at most $k$ is the arc set of a strongly connected digraph. It is proved that isomorphism testing of $k$-spanning tournaments is fixed-parameter tractable.