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COMBINATORICS
2006
119views more  COMBINATORICS 2006»
13 years 10 months ago
Relaxations of Ore's Condition on Cycles
A simple, undirected 2-connected graph G of order n belongs to class O(n,), 0, if 2 = n - . It is well known (Ore's theorem) that G is hamiltonian if = 0, in which case the 2...
Ahmed Ainouche
DM
2008
114views more  DM 2008»
13 years 10 months ago
Subdivisions of graphs: A generalization of paths and cycles
One of the basic results in graph theory is Dirac's theorem, that every graph of order n 3 and minimum degree n/2 is Hamiltonian. This may be restated as: if a graph of ord...
Ch. Sobhan Babu, Ajit A. Diwan
ENDM
2007
104views more  ENDM 2007»
13 years 10 months ago
Matching graphs of Hypercubes and Complete Bipartite Graphs
Kreweras’ conjecture [9] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle of Qd. We [5] proved this conjecture but here we present ...
Jirí Fink
ICALP
1994
Springer
14 years 2 months ago
Finding Even Cycles Even Faster
We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k 2, there is an O(V 2) time algorithm that decide...
Raphael Yuster, Uri Zwick
DM
2007
116views more  DM 2007»
13 years 10 months ago
The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...