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Title:
Counting K-4-subdivisions
Author: Miltzow, T ; Schmidt, JM ; Xia, MJ
Keyword: Counting K-4-subdivisions ; Cycles ; 3-connected graphs
Source: DISCRETE MATHEMATICS
Issued Date: 2015
Volume: 338, Issue:12, Pages:2387-2392
Indexed Type: SCI
Department: FU Berlin, Berlin, Germany. TU Ilmenau, Ilmenau, Germany. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100864, Peoples R China.
Abstract: A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K-4. As a generalization, we ask for the minimum number of K-4-subdivisions that are contained in every 3-connected graph on n vertices. We prove that there are Omega(n(3)) such K-4-subdivisions and show that the order of this bound is tight for infinitely many graphs. We further investigate a better bound in dependence on m and prove that the computational complexity of the problem of counting the exact number of K-4-subdivisions is OP-hard. (C) 2015 Elsevier B.V. All rights reserved.
English Abstract: A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K-4. As a generalization, we ask for the minimum number of K-4-subdivisions that are contained in every 3-connected graph on n vertices. We prove that there are Omega(n(3)) such K-4-subdivisions and show that the order of this bound is tight for infinitely many graphs. We further investigate a better bound in dependence on m and prove that the computational complexity of the problem of counting the exact number of K-4-subdivisions is OP-hard. (C) 2015 Elsevier B.V. All rights reserved.
Language: 英语
WOS ID: WOS:000359955700026
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17424
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Miltzow, T,Schmidt, JM,Xia, MJ. Counting K-4-subdivisions[J]. DISCRETE MATHEMATICS,2015-01-01,338(12):2387-2392.
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