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ARSCOM
2004
104views more  ARSCOM 2004»
14 years 11 months ago
Complete Minors in Cubic Graphs with few short Cycles and Random Cubic Graphs
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
Klas Markstrom
GC
2011
Springer
14 years 6 months ago
Ramsey Numbers of Some Bipartite Graphs Versus Complete Graphs
The Ramsey number r(H, Kn) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Tur´an number ex(m,...
Tao Jiang, Michael Salerno
DAM
2008
85views more  DAM 2008»
14 years 11 months ago
The competition numbers of complete tripartite graphs
For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition nu...
Suh-Ryung Kim, Yoshio Sano
RSA
2010
118views more  RSA 2010»
14 years 10 months ago
Weight of a link in a shortest path tree and the Dedekind Eta function
The weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generatin...
Piet Van Mieghem