Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Discrete Mathematics - Graph colouring and variations
A Helly theorem in weakly modular space
Discrete Mathematics
SIAM Journal on Discrete Mathematics
Dominating Cliques in Distance-Hereditary Graphs
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
A Linear-Time Algorithm for Finding a Central Vertex of a Chordal Graph
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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In a graph G=(V,E), the eccentricity e(v) of a vertex v is max{d(v,u): u ∈ V}. The center of a graph is the set of vertices with minimum eccentricity. A house-hole-domino-free (HHD-free) graph is a graph which does not contain the house, the domino, and holes (cycles of length at least five) as induced subgraphs. We present an algorithm which finds a central vertex of a HHD-free graph in O(Δ1.376|V|) time, where Δ is the maximum degree of a vertex of G. Its complexity is linear in the case of weak bipolarizable graphs, chordal graphs, and distance-hereditary graphs. The algorithm uses special metric and convexity properties of HHD-free graphs.