Minimum degree conditions for H-linked graphs

https://doi.org/10.1016/j.dam.2006.11.013Get rights and content
Under an Elsevier user license
open archive

Abstract

For a fixed multigraph H with vertices w1,,wm, a graph G is H-linked if for every choice of vertices v1,,vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs.

Given a connected multigraph H with k edges and minimum degree at least two and n7.5k, we determine the least integer d such that every n-vertex simple graph with minimum degree at least d is H-linked. This value D(H,n) appears to equal the least integer d such that every n-vertex graph with minimum degree at least d is b(H)-connected, where b(H) is the maximum number of edges in a bipartite subgraph of H.

Keywords

Extremal graph problems
Degree conditions
H-linked graphs

Cited by (0)

This work was supported by the NSF grants DMS-0099608 and DMS-0400498.

1

Research was also partially supported by Grants 99-01-00581 and 00-01-00916 of the Russian Foundation for Basic Research.