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RSA
2010
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13 years 10 months ago
Hamiltonicity thresholds in Achlioptas processes
In this paper we analyze the appearance of a Hamilton cycle in the following random process. The process starts with an empty graph on n labeled vertices. At each round we are pre...
Michael Krivelevich, Eyal Lubetzky, Benny Sudakov
SIAMDM
2008
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13 years 11 months ago
Hamilton Cycles in Planar Locally Finite Graphs
A classical theorem by Tutte assures the existence of a Hamilton cycle in every finite 4-connected planar graph. Extensions of this result to infinite graphs require a suitable co...
Henning Bruhn, Xingxing Yu
JCT
2007
76views more  JCT 2007»
13 years 11 months ago
Perfect matchings extend to Hamilton cycles in hypercubes
Kreweras’ conjecture [1] asserts that any perfect matching of the hypercube Qd, d ≥ 2, can be extended to a Hamilton cycle. We prove this conjecture.
Jirí Fink
COMBINATORICS
2007
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13 years 11 months ago
Maximum Cardinality 1-Restricted Simple 2-Matchings
A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We co...
David Hartvigsen
DM
2006
84views more  DM 2006»
13 years 11 months ago
Hamilton cycles in digraphs of unitary matrices
We conjecture new sufficient conditions for a digraph to have a Hamilton cycle. In view of applications, the conjecture is of interest in the areas where unitary matrices are of i...
Gregory Gutin, Arash Rafiey, Simone Severini, Ande...