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» Edge clique graphs and some classes of chordal graphs
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GC
2007
Springer
14 years 9 months ago
On the Maximum Number of Cliques in a Graph
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m ...
David R. Wood
SODA
2012
ACM
213views Algorithms» more  SODA 2012»
12 years 12 months ago
Expanders are universal for the class of all spanning trees
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
DM
2006
92views more  DM 2006»
14 years 9 months ago
Minimal triangulations of graphs: A survey
Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph. In this paper we study minimal tr...
Pinar Heggernes
ICALP
2009
Springer
15 years 9 months ago
Elimination Graphs
A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, whi...
Yuli Ye, Allan Borodin
JCT
2007
146views more  JCT 2007»
14 years 9 months ago
Laplacian spectral bounds for clique and independence numbers of graphs
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
Mei Lu, Huiqing Liu, Feng Tian