Complete graph immersions and minimum degree
Combinatorics
2015-12-03 v1
Abstract
An immersion of a graph H in another graph G is a one-to-one mapping phi:V(H)->V(G) and a collection of edge-disjoint paths in G, one for each edge of H, such that the path P_{uv} corresponding to the edge uv has endpoints phi(u) and phi(v). The immersion is strong if the paths P_{uv} are internally disjoint from phi(V(H)). We prove that every simple graph of minimum degree at least 11t+7 contains a strong immersion of the complete graph K_t. This improves on previously known bound of minimum degree at least 200t obtained by DeVos et al.
Keywords
Cite
@article{arxiv.1512.00513,
title = {Complete graph immersions and minimum degree},
author = {Zdeněk Dvořák and Liana Yepremyan},
journal= {arXiv preprint arXiv:1512.00513},
year = {2015}
}
Comments
12 pages, 1 figure