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arXiv · 1907.08447

Fractional decompositions and the smallest-eigenvalue separation

Fiachra Knox·Bojan Mohar
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Abstract

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 [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.

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Fiachra Knox, Bojan Mohar. 2019-07-19. Fractional decompositions and the smallest-eigenvalue separation. https://arxiv.org/abs/1907.08447

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