Graphs with restricted valency and matching number

Niranjan Balachandran; Niraj Khare

Graphs with restricted valency and matching number

Combinatorics 2007-05-23 v1

Authors: Niranjan Balachandran , Niraj Khare

Abstract

Consider the family of all finite graphs with maximum degree $\Delta(G)<d$ and matching number $\nu(G)<m$ . In this paper we give a new proof to obtain the exact upper bound for the number of edges in such graphs and also characterize all the cases when the maximal graph is unique. We also provide a new proof of Gallai's lemma concerning factor critical graphs.

Keywords

graph pebbling graph theory graph coloring

Cite

@article{arxiv.math/0611842,
  title  = {Graphs with restricted valency and matching number},
  author = {Niranjan Balachandran and Niraj Khare},
  journal= {arXiv preprint arXiv:math/0611842},
  year   = {2007}
}

Comments

13 pages

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