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On the existence of -partite or -free total domination edge-critical graphs

โœ Scribed by Teresa W. Haynes; Michael A. Henning; Lucas C. van der Merwe; Anders Yeo


Book ID
111712854
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
304 KB
Volume
311
Category
Article
ISSN
0012-365X

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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