Note on the Diameter of Path-Pairable Graphs

Gabor Meszaros

Note on the Diameter of Path-Pairable Graphs

Combinatorics 2014-07-29 v2

Authors: Gabor Meszaros

Abstract

A graph on $2k$ vertices is path-pairable if for any pairing of the vertices the pairs can be joined by edge-disjoint paths. The so far known families of path-pairable graphs have diameter of length at most 3. In this paper we present an infinite family of path-pairable graphs with diameter $d(G)=O(\sqrt{n})$ where $n$ denotes the number of vertices of the graph. We prove that our example is extremal up to a constant factor.

Keywords

graph theory graph pebbling graph cycles

Cite

@article{arxiv.1401.7931,
  title  = {Note on the Diameter of Path-Pairable Graphs},
  author = {Gabor Meszaros},
  journal= {arXiv preprint arXiv:1401.7931},
  year   = {2014}
}

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