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COMBINATORICS
2006
119views more  COMBINATORICS 2006»
15 years 6 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»
15 years 6 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»
15 years 6 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
15 years 10 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»
15 years 6 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. ...