EJC
2007
13 years 11 months ago
2007
Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n â...
JGT
2006
13 years 11 months ago
2006
It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for...
JCT
2006
13 years 11 months ago
2006
Kuipers and Veldman conjectured that any 3-connected claw-free graph with order and minimum degree +6 10 is Hamiltonian for sufficiently large. In this paper, we prove that if...
DM
2007
13 years 11 months ago
2007
By Petersen’s theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing ...
JCT
2008
13 years 11 months ago
2008
The old well-known result of Chartrand, Kaugars and Lick [1] says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G - v is still k-connec...
JCT
2008
13 years 11 months ago
2008
A conjecture by Bollob
COMBINATORICS
2006
13 years 11 months ago
2006
We prove the following extension of an old result of Andr
GC
2008
Springer
13 years 11 months ago
2008
Springer
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...
DM
2008
13 years 11 months ago
2008
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...
CORR
2010
Springer
13 years 11 months ago
2010
Springer
We study Maker-Breaker games played on the edge set of a random graph. Specifically, we consider the random graph process and analyze the first time in a typical random graph proc...