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Degree Conditions for H-Linked Digraphs

Published online by Cambridge University Press:  08 August 2013

MICHAEL FERRARA ,
MICHAEL JACOBSON  and
FLORIAN PFENDER
MICHAEL FERRARA
Affiliation:
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80217, USA (e-mail: michael.ferrara@ucdenver.edu, michael.jacobson@ucdenver.edu, florian.pfender@ucdenver.edu)
MICHAEL JACOBSON
Affiliation:
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80217, USA (e-mail: michael.ferrara@ucdenver.edu, michael.jacobson@ucdenver.edu, florian.pfender@ucdenver.edu)
FLORIAN PFENDER
Affiliation:
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80217, USA (e-mail: michael.ferrara@ucdenver.edu, michael.jacobson@ucdenver.edu, florian.pfender@ucdenver.edu)
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Abstract

Given a (multi)digraph H, a digraph D is H-linked if every injective function ι:V(H) → V(D) can be extended to an H-subdivision. In this paper, we give sharp degree conditions that ensure a sufficiently large digraph D is H-linked for arbitrary H. The notion of an H-linked digraph extends the classes of m-linked, m-ordered and strongly m-connected digraphs.

First, we give sharp minimum semi-degree conditions for H-linkedness, extending results of Kühn and Osthus on m-linked and m-ordered digraphs. It is known that the minimum degree threshold for an undirected graph to be H-linked depends on a partition of the (undirected) graph H into three parts. Here, we show that the corresponding semi-degree threshold for H-linked digraphs depends on a partition of H into as many as nine parts.

We also determine sharp Ore–Woodall-type degree-sum conditions ensuring that a digraph D is H-linked for general H. As a corollary, we obtain (previously undetermined) sharp degree-sum conditions for m-linked and m-ordered digraphs.

Keywords

Primary 05C2005C38Secondary 05C40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 5 , September 2013 , pp. 684 - 699
Copyright
Copyright © Cambridge University Press 2013 

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