EJC
2007
13 years 9 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 9 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 9 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 9 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 9 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 9 months ago
2008
A conjecture by Bollob
COMBINATORICS
2006
13 years 9 months ago
2006
We prove the following extension of an old result of Andr
GC
2008
Springer
13 years 9 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 9 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 9 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...