A graph is said to be P4-connected if for every partition of its vertices into two nonempty disjoint sets, some P4 in the graph contains vertices from both sets in the partition. A P4-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 Pi-connected if and only if each pair of vertices is connected by a P4-chain. Our proof relies, in part, on a linear-time algorithm that, given two distinct vertices, exhibits a P4-chain connecting them. In addition to shedding new light on the structure of P4-connected graphs, our result extends a previously known theorem about the P4-structure of unbreakable graphs.
CITATION STYLE
Babel, L., & Olariu, S. (1997). A new characterization of P4 - Connected graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1197 LNCS, pp. 17–30). https://doi.org/10.1007/3-540-62559-3_3
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