Degree Conditions for H-Linked Digraphs

2013 Combinatorics, probability & computing  
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 assure 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
more » ... ed 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 assuring 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.
doi:10.1017/s0963548313000278 fatcat:kab4kbgouvcjzb5wx4gj44yy4e