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http://hdl.handle.net/10012/6464
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| Title: | 2-crossing critical graphs with a V8 minor |
| Authors: | Austin, Beth Ann |
| Keywords: | graph theory
crossing number |
| Approved Date: | 17-Jan-2012 |
| Date Submitted: | 2012 |
| Abstract: | The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a crossing number less than k.
The set of 1-crossing critical graphs is is determined by Kuratowski’s Theorem to be {K5, K3,3}. Work has been done to approach the problem of classifying all 2-crossing critical graphs. The graph V2n is a cycle on 2n vertices with n intersecting chords. The only remaining graphs to find in the classification of 2-crossing critical graphs are those that are 3-connected with a V8 minor but no V10 minor.
This paper seeks to fill some of this gap by defining and completely describing a class of graphs called fully covered. In addition, we examine other ways in which graphs may be 2-crossing critical. This discussion classifies all known examples of 3-connected, 2-crossing critical graphs with a V8 minor but no V10 minor. |
| Program: | Combinatorics and Optimization |
| Department: | Combinatorics and Optimization |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/6464 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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