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EJC
2007
13 years 9 months ago
Perfect packings with complete graphs minus an edge
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...
Oliver Cooley, Daniela Kühn, Deryk Osthus
JGT
2006
97views more  JGT 2006»
13 years 9 months ago
Matchings in hypergraphs of large minimum degree
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...
Daniela Kühn, Deryk Osthus
JCT
2006
102views more  JCT 2006»
13 years 9 months ago
Hamiltonicity in 3-connected claw-free graphs
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...
Hong-Jian Lai, Yehong Shao, Mingquan Zhan
DM
2007
149views more  DM 2007»
13 years 9 months ago
Even subgraphs of bridgeless graphs and 2-factors of line graphs
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 ...
Bill Jackson, Kiyoshi Yoshimoto
JCT
2008
70views more  JCT 2008»
13 years 9 months ago
Connectivity keeping edges in graphs with large minimum degree
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...
Shinya Fujita, Ken-ichi Kawarabayashi
JCT
2008
109views more  JCT 2008»
13 years 9 months ago
Spanning 3-colourable subgraphs of small bandwidth in dense graphs
A conjecture by Bollob
Julia Böttcher, Mathias Schacht, Anusch Taraz
COMBINATORICS
2006
97views more  COMBINATORICS 2006»
13 years 9 months ago
H-Free Graphs of Large Minimum Degree
We prove the following extension of an old result of Andr
Noga Alon, Benny Sudakov
GC
2008
Springer
13 years 9 months ago
Domination in Graphs of Minimum Degree at least Two and Large Girth
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 ...
Christian Löwenstein, Dieter Rautenbach
DM
2008
114views more  DM 2008»
13 years 9 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
CORR
2010
Springer
60views Education» more  CORR 2010»
13 years 9 months ago
Hitting time results for Maker-Breaker games
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...
Sonny Ben-Shimon, Asaf Ferber, Dan Hefetz, Michael...