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Title: Degenerate Distributed Feedback Photonic Structure With Two Gratings Exhibiting Degenerate Band Edge
Award ID(s):
1711975
PAR ID:
10421493
Author(s) / Creator(s):
;
Date Published:
Journal Name:
IEEE Photonics Technology Letters
Volume:
35
Issue:
4
ISSN:
1041-1135
Page Range / eLocation ID:
187 to 190
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract

    Alinear forestis a union of vertex‐disjoint paths, and thelinear arboricityof a graph , denoted by , is the minimum number of linear forests into which the edge set of can be partitioned. Clearly, for a graph with maximum degree . On the other hand, theLinear Arboricity Conjecturedue to Akiyama, Exoo, and Harary from 1981 asserts that for every graph . This conjecture has been verified for planar graphs and graphs whose maximum degree is at most , or is equal to or . Given a positive integer , a graph is ‐degenerateif it can be reduced to a trivial graph by successive removal of vertices with a degree at most . We prove that for any ‐degenerate graph provided .

     
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