Going critical : an investigation of diameter -critical graphs

Going critical : an investigation of diameter -critical graphs

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We define a graph G=(V, E) with m=\E\ edges, n=\V\ vertices, maximum degree D, and diameter d, to be d-critical if it has the property that for any edge e G E, the graph G — e has diameter > d. We explore some results relating to a conjecture on the maximum possible number of edges in a 2-critic...

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Main Author: Madden, Joshua
Format: Others
Language:English
Published: 2009
Online Access:http://hdl.handle.net/2429/10030
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spelling ndltd-UBC-oai-circle.library.ubc.ca-2429-100302018-01-05T17:35:05Z Going critical : an investigation of diameter -critical graphs Madden, Joshua We define a graph G=(V, E) with m=\E\ edges, n=\V\ vertices, maximum degree D, and diameter d, to be d-critical if it has the property that for any edge e G E, the graph G — e has diameter > d. We explore some results relating to a conjecture on the maximum possible number of edges in a 2-critical graph. We also present efficient algorithms for identifying spanning d-critical subgraphs of graphs having diameter d where d=2 or d=3. The algorithm for d=2 runs in 0(mn), and the algorithm for d=3 runs in 0(mnD). Science, Faculty of Mathematics, Department of Graduate 2009-07-03 2009-07-03 1999 1999-05 Text Thesis/Dissertation http://hdl.handle.net/2429/10030 eng For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. 2673799 bytes application/pdf
collection NDLTD
language English
format Others
sources NDLTD
description We define a graph G=(V, E) with m=\E\ edges, n=\V\ vertices, maximum degree D, and diameter d, to be d-critical if it has the property that for any edge e G E, the graph G — e has diameter > d. We explore some results relating to a conjecture on the maximum possible number of edges in a 2-critical graph. We also present efficient algorithms for identifying spanning d-critical subgraphs of graphs having diameter d where d=2 or d=3. The algorithm for d=2 runs in 0(mn), and the algorithm for d=3 runs in 0(mnD). === Science, Faculty of === Mathematics, Department of === Graduate
author Madden, Joshua
spellingShingle Madden, Joshua
Going critical : an investigation of diameter -critical graphs
author_facet Madden, Joshua
author_sort Madden, Joshua
title Going critical : an investigation of diameter -critical graphs
title_short Going critical : an investigation of diameter -critical graphs
title_full Going critical : an investigation of diameter -critical graphs
title_fullStr Going critical : an investigation of diameter -critical graphs
title_full_unstemmed Going critical : an investigation of diameter -critical graphs
title_sort going critical : an investigation of diameter -critical graphs
publishDate 2009
url http://hdl.handle.net/2429/10030
work_keys_str_mv AT maddenjoshua goingcriticalaninvestigationofdiametercriticalgraphs
_version_ 1718588048713711616

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