Displaying similar documents to “Interval partitions and pair interactions”

Structural Properties of Recursively Partitionable Graphs with Connectivity 2

Olivier Baudon, Julien Bensmail, Florent Foucaud, Monika Pilśniak (2017)

Discussiones Mathematicae Graph Theory

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A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1, . . . , np) of |V (G)| there exists a partition (V1, . . . , Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition...

The interval function of a connected graph and a characterization of geodetic graphs

Ladislav Nebeský (2001)

Mathematica Bohemica

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The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize...