Open Access
July 2015 Intrinsic linking in directed graphs
Joel Stephen Foisy, Hugh Nelson Howards, Natalie Rose Rich
Osaka J. Math. 52(3): 817-833 (July 2015).


We extend the notion of intrinsic linking to directed graphs. We give methods of constructing intrinsically linked directed graphs, as well as complicated directed graphs that are not intrinsically linked. We prove that the double directed version of a graph $G$ is intrinsically linked if and only if $G$ is intrinsically linked. One Corollary is that $\overline{J_{6}}$, the complete symmetric directed graph on 6 vertices (with 30 directed edges), is intrinsically linked. We further extend this to show that it is possible to find a subgraph of $\overline{J_{6}}$ by deleting 6 edges that is still intrinsically linked, but that no subgraph of $\overline{J_{6}}$ obtained by deleting 7 edges is intrinsically linked. We also show that $\overline{J_{6}}$ with an arbitrary edge deleted is intrinsically linked, but if the wrong two edges are chosen, $\overline{J_{6}}$ with two edges deleted can be embedded linklessly.


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Joel Stephen Foisy. Hugh Nelson Howards. Natalie Rose Rich. "Intrinsic linking in directed graphs." Osaka J. Math. 52 (3) 817 - 833, July 2015.


Published: July 2015
First available in Project Euclid: 17 July 2015

zbMATH: 1337.57016
MathSciNet: MR3370476

Primary: 05C10 , 57M15 , 57M25

Rights: Copyright © 2015 Osaka University and Osaka City University, Departments of Mathematics

Vol.52 • No. 3 • July 2015
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