Degenerate Distributed Feedback Photonic Structure With Two Gratings Exhibiting Degenerate Band Edge
- Award ID(s):
- 1711975
- PAR ID:
- 10421493
- 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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Abstract A
linear forest is a union of vertex‐disjoint paths, and thelinear arboricity of 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 Conjecture due 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 ‐degenerate if 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 .