Doubly lexical orderings of matrices
SIAM Journal on Computing
Clique graphs and Helly graphs
Journal of Combinatorial Theory Series B
Neighborhood subtree tolerance graphs
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On graph powers for leaf-labeled trees
Journal of Algorithms
Discrete Applied Mathematics
Efficient Parallel and Linear Time Sequential Split Decomposition (Extended Abstract)
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Structure and linear time recognition of 3-leaf powers
Information Processing Letters
Strictly chordal graphs are leaf powers
Journal of Discrete Algorithms
Structure and linear-time recognition of 4-leaf powers
ACM Transactions on Algorithms (TALG)
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Ptolemaic graphs and interval graphs are leaf powers
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences
Discrete Applied Mathematics
Hi-index | 5.23 |
In a graph, a vertex is simplicial if its neighborhood is a clique. For an integer k=1, a graph G=(V"G,E"G) is the k-simplicial power of a graph H=(V"H,E"H) (H a root graph of G) if V"G is the set of all simplicial vertices of H, and for all distinct vertices x and y in V"G, xy@?E"G if and only if the distance in H between x and y is at most k. This concept generalizes k-leaf powers introduced by Nishimura, Ragde and Thilikos which were motivated by the search for underlying phylogenetic trees; k-leaf powers are the k-simplicial powers of trees. Recently, a lot of work has been done on k-leaf powers and their roots as well as on their variants phylogenetic roots and Steiner roots. For k@?5, k-leaf powers can be recognized in linear time, and for k@?4, structural characterizations are known. For k=6, the recognition and characterization problems of k-leaf powers are still open. Since trees and block graphs (i.e., connected graphs whose blocks are cliques) have very similar metric properties, it is natural to study k-simplicial powers of block graphs. We show that leaf powers of trees and simplicial powers of block graphs are closely related, and we study simplicial powers of other graph classes containing all trees such as ptolemaic graphs and strongly chordal graphs.