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COMBINATORICS
2007
14 years 10 months ago
2007
In this note we present a short proof of the following result, which is a slight extension of a nice 2005 theorem by Kano and Yu. Let e be an edge of an rregular graph G. If G has...
JCT
2006
14 years 10 months ago
2006
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....
DAM
2000
14 years 9 months ago
2000
A graph G is chordal if it contains no chordless cycle of length at least four and is k-chordal if a longest chordless cycle in G has length at most k. In this note it is proved t...
ORL
2007
14 years 9 months ago
2007
We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k. Finally, we propose some ap...
SIAMDM
2008
14 years 9 months ago
2008
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...