Generating the maximum spanning trees of a weighted graph
Journal of Algorithms
Clique Graphs of Chordal and Path Graphs
SIAM Journal on Discrete Mathematics
Forbidden induced subgraphs for line graphs
Discrete Mathematics
Discrete Mathematics
SIAM Journal on Discrete Mathematics
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Restricted circular-arc graphs and clique cycles
Discrete Mathematics
Line Graphs of Helly Hypergraphs
SIAM Journal on Discrete Mathematics
Graphs and Hypergraphs
The complexity of clique graph recognition
Theoretical Computer Science
Reduced clique graphs of chordal graphs
European Journal of Combinatorics
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Given integers m"1,...,m"@?, the weighted clique graph of G is the clique graph K(G), in which there is a weight assigned to each complete set S of size m"i of K(G), for each i=1,...,@?. This weight equals the cardinality of the intersection of the cliques of G corresponding to S. We characterize weighted clique graphs in similar terms as Roberts and Spencer's characterization of clique graphs. Further we characterize several classical graph classes in terms of their weighted clique graphs, providing a common framework for describing some different well-known classes of graphs, as hereditary clique-Helly graphs, split graphs, chordal graphs, interval graphs, proper interval graphs, line graphs, among others.