NDLI: Contractible Elements in Graphs and Matroids

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Contractible Elements in Graphs and Matroids

Content Provider	Scilit
Author	Wu, Haidong
Copyright Year	2003
Description	Let G be a simple 3-connected graph with at least five vertices. Tutte [13] showed that G has at least one contractible edge. Thomassen [11] gave a simple proof of this fact and showed that contractible edges have many applications. In this paper, we show that there are at most vertices that are not incident to contractible edges in a 3-connected graph G. This bound is best-possible. We also show that if a vertex v is not incident to any contractible edge in G, then v has at least four neighbours having degree three, and each such neighbour is incident to exactly two contractible edges. We give short proofs of several results on contractible edges in 3-connected graphs as well. We also study the contractible elements for k-connected matroids. We partially solve an open problem for regular matroids.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5556F945B4E534D2A8F017DE7E82BD5B/S0963548302005497a.pdf/div-class-title-contractible-elements-in-graphs-and-matroids-div.pdf
Ending Page	465
Page Count	9
Starting Page	457
ISSN	09635483
e-ISSN	14692163
DOI	10.1017/s0963548302005497
Journal	Combinatorics, Probability and Computing
Issue Number	4
Volume Number	12
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2003-07-01
Access Restriction	Open
Subject Keyword	Combinatorics, Probability and Computing Literary Studies Simple Proof connected Matroids connected Graph Contractible Elements Results Oncontractible Edge Contractible Edge Onecontractible Edge Regular Matroids connected Graphg Avertex V Contractible Edge Ing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics

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