Abstract
A graph is said to be P 4-connected if for every partition of its vertices into two nonempty disjoint sets, some P 4 in the graph contains vertices from both sets in the partition. A P 4-chain is a sequence of vertices such that every four consecutive ones induce a P 4. The main result of this work states that a graph is P 4-connected if and only if each pair of vertices is connected by a P 4chain. Our proof relies, in part, on a linear-time algorithm that, given two distinct vertices, exhibits a P 4-chain connecting them. In addition to shedding new light on the structure of P 4-connected graphs, our result extends a previously known theorem about the P 4-structure of unbreakable graphs.
This author was supported by the Deutsche Forschungsgemeinschaft (DFG)
This author was supported in part by NSF grant CCR-94-07180 and by ONR grant N00014-95-1-0779.
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© 1997 Springer-Verlag Berlin Heidelberg
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Babel, L., Olariu, S. (1997). A new characterization of P 4-connected graphs. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_3
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DOI: https://doi.org/10.1007/3-540-62559-3_3
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