Show simple item record

dc.contributor.authorArroyo Guevara, Alan Marcelo 17:51:23 (GMT) 17:51:23 (GMT)
dc.description.abstractThe crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of a graph. A graph $G$ is $k$-crossing-critical if it has crossing number at least $k$, and any subgraph of $G$ has crossing number less than $k$. A consequence of Kuratowski's theorem is that 1-critical graphs are subdivisions of $K_{3,3}$ and $K_{5}$. The graph $V_{2n}$ is a $2n$-cycle with $n$ diameters. Bokal, Oporowski, Richter and Salazar found in \cite{bigpaper} all the critical graphs except the ones that contain a $V_{8}$ minor and no $V_{10}$ minor. We show that a 4-connected graph $G$ has crossing number at least 2 if and only if for each pair of disjoint edges there are two disjoint cycles containing them. Using a generalization of this result we found limitations for the 2-crossing-critical graphs remaining to classify. We showed that peripherally 4-connected 2-crossing-critical graphs have at most 4001 vertices. Furthermore, most 3-connected 2-crossing-critical graphs are obtainable by small modifications of the peripherally 4-connected ones.en
dc.publisherUniversity of Waterlooen
dc.subjectgraph theoryen
dc.subjectcrossing numbersen
dc.subjectdisjoint pathsen
dc.subjectcrossing criticalen
dc.titleOn 2-crossing-critical graphs with a V8-minoren
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages