A new method is introduced for bounding the separation between the value of $-k$ and the smallest eigenvalue of a non-bipartite $k$-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 [Electronic J. Combin. 26(2) (2019), #P2.41] about the smallest eigenvalue of non-bipartite distance-regular graphs.
@article{10_37236_8833,
author = {Fiachra Knox and Bojan Mohar},
title = {Fractional decompositions and the smallest-eigenvalue separation},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8833},
zbl = {1428.05196},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8833/}
}
TY - JOUR
AU - Fiachra Knox
AU - Bojan Mohar
TI - Fractional decompositions and the smallest-eigenvalue separation
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8833/
DO - 10.37236/8833
ID - 10_37236_8833
ER -
%0 Journal Article
%A Fiachra Knox
%A Bojan Mohar
%T Fractional decompositions and the smallest-eigenvalue separation
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8833/
%R 10.37236/8833
%F 10_37236_8833
Fiachra Knox; Bojan Mohar. Fractional decompositions and the smallest-eigenvalue separation. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8833
