Extending partial automorphisms of $n$-partite tournaments
Abstract
We prove that for every $n\geq 2$ the class of all finite $n$-partite tournaments (orientations of complete $n$-partite graphs) has the extension property for partial automorphisms, that is, for every finite $n$-partite tournament $G$ there is a finite $n$-partite tournament $H$ such that every isomorphism of induced subgraphs of $G$ extends to an automorphism of $H$. Our constructions are purely combinatorial (whereas many earlier EPPA results use deep results from group theory) and extend to other classes such as the class of all finite semi-generic tournaments.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1903.07476
- arXiv:
- arXiv:1903.07476
- Bibcode:
- 2019arXiv190307476H
- Keywords:
-
- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- Mathematics - Group Theory;
- Primary: 05C20;
- 05C60;
- 05E18;
- Secondary: 20B25;
- G.2.2;
- F.4.1
- E-Print:
- 5 pages, extended abstract