Universality of intervals of line graph order
Abstract
We prove that for every $d\geq 3$ the homomorphism order of the class of line graphs of finite graphs with maximal degree $d$ is universal. This means that every finite or countably infinite partially ordered set may be represented by line graphs of graphs with maximal degree $d$ ordered by the existence of a homomorphism.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.3736
- arXiv:
- arXiv:1402.3736
- Bibcode:
- 2014arXiv1402.3736F
- Keywords:
-
- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- 05C60;
- 05C76;
- 06A06;
- G.2.2
- E-Print:
- 13 pages, 8 figures, accepted to European Journal of Combinatorics