English

Fractional decompositions and the smallest-eigenvalue separation

Combinatorics 2019-07-22 v1

Abstract

A new method is introduced for bounding the separation between the value of k-k and the smallest eigenvalue of a non-bipartite kk-regular graph. The method is based on fractional decompositions of graphs. As a consequence we obtain a very short proof of a generalization and strengthening of a recent result of Qiao, Jing, and Koolen [Non-bipartite distance-regular graphs with a small smallest eigenvalue, Electronic J. Combin. 26(2) (2019), P2.41] about the smallest eigenvalue of non-bipartite distance-regular graphs.

Keywords

Cite

@article{arxiv.1907.08447,
  title  = {Fractional decompositions and the smallest-eigenvalue separation},
  author = {Fiachra Knox and Bojan Mohar},
  journal= {arXiv preprint arXiv:1907.08447},
  year   = {2019}
}
R2 v1 2026-06-23T10:25:08.801Z