Abstract
Determining the diameter of a graph is a fundamental graph operation, yet no efficient (i.e. quadratic time) algorithm is known. In this paper, we examine the diameter problem on chordal and AT-free graphs and show that a very simple (linear time) 2-sweep Lex-BFS algorithm identifies a vertex of maximum eccentricity unless the given graph has a specified induced subgraph (it was previously known that a single Lex-BFS algorithm is guaranteed to end at a vertex that is within 1 of the diameter for chordal and AT-free graphs). As a consequence of the forbidden induced subgraph result on chordal graphs, our algorithm is guaranteed to work optimally for directed path graphs (it was previously known that a single LexBFS algorithm is guaranteed to work optimally for interval graphs).
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© 1998 Springer-Verlag Berlin Heidelberg
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Corneil, D.G., Dragan, F.F., Habib, M., Paul, C. (1998). Diameter Determination on Restricted Graph Families. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_16
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DOI: https://doi.org/10.1007/10692760_16
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