Toughness and factors in graphs
The author proved independently, every 2-tough graph is hamiltonian (3), that if G is a K-tough graph with n vertices and if kn is even then G has a k-factor (4) is best possible by showing that for every positive integer k and for every positive $ varepsilon$ there is a (k-$ varepsilon$)-tough grap...
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ndltd-LACETR-oai-collectionscanada.gc.ca-QMM.596162014-02-13T04:07:35ZToughness and factors in graphsTsikopoulos, NicholasMathematics.The author proved independently, every 2-tough graph is hamiltonian (3), that if G is a K-tough graph with n vertices and if kn is even then G has a k-factor (4) is best possible by showing that for every positive integer k and for every positive $ varepsilon$ there is a (k-$ varepsilon$)-tough graph G with no k-factor; furthermore, if k is odd then G can be made to have an even number of vertices; this result makes chapter 1 of the present thesis.Enomoto elaborated further on the subject and gave two results, in (4) and (5) respectively, which are improvements over (4):(5) provided that k$ vert$G$ vert$ is even and $ vert$G$ vert sbsp{=}{>}$ k + 1, G has a k-factor if, for each set S of vertices, G-S has at most $ vert$S$ vert$/k + 7/8 components; and (6) provided that k$ vert$G$ vert$ is even and $ vert$G$ vert sbsp{=}{>}$ k$ sp{2}$ + 1, G has a k-factor if, for each set S of vertices, G-S has at most $ vert$S$ vert$/k + 1 components. The proofs of (4), (5) and (6) make chapters 2, 3 and 4 respectively.McGill University1987Electronic Thesis or Dissertationapplication/pdfenalephsysno: 001067771proquestno: AAIMM64102Theses scanned by UMI/ProQuest.All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated.Master of Science (School of Computer Science.) http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=59616 |
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Mathematics. Tsikopoulos, Nicholas Toughness and factors in graphs |
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The author proved independently, every 2-tough graph is hamiltonian (3), that if G is a K-tough graph with n vertices and if kn is even then G has a k-factor (4) is best possible by showing that for every positive integer k and for every positive $ varepsilon$ there is a (k-$ varepsilon$)-tough graph G with no k-factor; furthermore, if k is odd then G can be made to have an even number of vertices; this result makes chapter 1 of the present thesis. === Enomoto elaborated further on the subject and gave two results, in (4) and (5) respectively, which are improvements over (4): === (5) provided that k$ vert$G$ vert$ is even and $ vert$G$ vert sbsp{=}{>}$ k + 1, G has a k-factor if, for each set S of vertices, G-S has at most $ vert$S$ vert$/k + 7/8 components; and (6) provided that k$ vert$G$ vert$ is even and $ vert$G$ vert sbsp{=}{>}$ k$ sp{2}$ + 1, G has a k-factor if, for each set S of vertices, G-S has at most $ vert$S$ vert$/k + 1 components. The proofs of (4), (5) and (6) make chapters 2, 3 and 4 respectively. |
author |
Tsikopoulos, Nicholas |
author_facet |
Tsikopoulos, Nicholas |
author_sort |
Tsikopoulos, Nicholas |
title |
Toughness and factors in graphs |
title_short |
Toughness and factors in graphs |
title_full |
Toughness and factors in graphs |
title_fullStr |
Toughness and factors in graphs |
title_full_unstemmed |
Toughness and factors in graphs |
title_sort |
toughness and factors in graphs |
publisher |
McGill University |
publishDate |
1987 |
url |
http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=59616 |
work_keys_str_mv |
AT tsikopoulosnicholas toughnessandfactorsingraphs |
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