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» On almost self-complementary graphs
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COMBINATORICS
2007
72views more  COMBINATORICS 2007»
13 years 4 months ago
On Self-Complementary Cyclic Packing of Forests
A graph is self-complementary if it is isomorphic to its complement. In this paper we prove that every forest of order 4p and size less than 3p is a subgraph of a self-complementa...
A. Pawel Wojda, Mariusz Wozniak, Irmina A. Ziolo
SIAMCOMP
2011
12 years 11 months ago
A Combinatorial Construction of Almost-Ramanujan Graphs Using the Zig-Zag Product
Reingold, Vadhan and Wigderson [21] introduced the graph zig-zag product. This product combines a large graph and a small graph into one graph, such that the resulting graph inher...
Avraham Ben-Aroya, Amnon Ta-Shma
STOC
2002
ACM
121views Algorithms» more  STOC 2002»
14 years 5 months ago
Almost all graphs with average degree 4 are 3-colorable
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...
Dimitris Achlioptas, Cristopher Moore
RSA
2011
126views more  RSA 2011»
12 years 11 months ago
Local resilience of almost spanning trees in random graphs
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...
József Balogh, Béla Csaba, Wojciech ...
WG
2004
Springer
13 years 10 months ago
Partitioning a Weighted Graph to Connected Subgraphs of Almost Uniform Size
Abstract. Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wish to partition G into connected components...
Takehiro Ito, Xiao Zhou, Takao Nishizeki