109views more  SIAMDM 2010»
9 years 15 days ago
Ends and Vertices of Small Degree in Infinite Minimally k-(Edge)-Connected Graphs
Bounds on the minimum degree and on the number of vertices attaining it have been much studied for finite edge-/vertex-minimally kconnected/k-edge-connected graphs. We give an ove...
Maya Stein
91views more  SIAMDM 2010»
9 years 15 days ago
Embedding into Bipartite Graphs
Abstract. The conjecture of Bollob
Julia Böttcher, Peter Heinig, Anusch Taraz
152views more  JGT 2010»
9 years 16 days ago
Cycles of even lengths modulo k
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
Ajit A. Diwan
69views Education» more  CORR 2010»
9 years 21 days ago
Embedding a Forest in a Graph
For p 1, we prove that every forest with p trees whose sizes are a1, . . . , ap can be embedded in any graph containing at least p i=1(ai + 1) vertices and having minimum degree ...
Mark K. Goldberg, Malik Magdon-Ismail
9 years 24 days ago
Bounds on the k-domination number of a graph
The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove t...
Ermelinda DeLaViña, Wayne Goddard, Michael ...
9 years 3 months ago
A randomized embedding algorithm for trees
In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a "self-avoiding tree-indexed random ...
Benny Sudakov, Jan Vondrák
96views more  SIAMDM 2010»
9 years 4 months ago
Note on Bipartite Graph Tilings
Let s < t be two fixed positive integers. We study what are the minimum degree conditions for a bipartite graph G, with both color classes of size n = k(s + t), which ensure t...
Jan Hladký, Mathias Schacht
83views more  JGT 2010»
9 years 4 months ago
Forbidden subgraphs and the existence of a 2-factor
In 1996, Ota and Tokuda showed that a star-free graph with sufficiently high minimum degree admits a 2-factor. More recently it was shown that the minimum degree condition can be ...
Robert E. L. Aldred, Jun Fujisawa, Akira Saito
90views more  JGT 2010»
9 years 4 months ago
The rainbow connection of a graph is (at most) reciprocal to its minimum degree
An edge-colored graph G is rainbow edge-connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, deno...
Michael Krivelevich, Raphael Yuster
93views more  COMBINATORICS 1999»
9 years 5 months ago
Induced Complete h-partite Graphs in Dense Clique-less Graphs
It is proven that for every fixed h, a and b, a graph with n vertices and minimum degree at least h-1 h n, which contains no copy of Kb (the complete graph with b vertices), conta...
Eldar Fischer