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A proof of unimodality on the numbers of connected spanning subgraphs in an -vertex graph with at least edges

โœ Scribed by Peng Cheng; Shigeru Masuyama


Book ID
108112855
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
721 KB
Volume
158
Category
Article
ISSN
0166-218X

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Tight upper bound on the number of edges
โœ Zhi-Zhong Chen; Shiqing Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 68 KB

We show that an n-vertex bipartite K 3,3 -free graph with n 3 has at most 2n -4 edges and that an n-vertex bipartite K 5 -free graph with n 5 has at most 3n -9 edges. These bounds are also tight. We then use the bound on the number of edges in a K 3,3 -free graph to extend two known NC algorithms fo