We prove that the list chromatic index of a graph of maximum degree and treewidth ≤ √2 − 3 is ; and that the total chromatic number of a graph of maximum degree and treewidth ≤ /3 + 1 is + 1. This improves results by Meeks and Scott. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 81: 272–282, 2016

We prove that the list chromatic index of a graph of maximum degree ∆ and treewidth ≤ √ 2∆ − 3 is ∆; and that the total chromatic number of a graph of maximum degree ∆ and treewidth ≤ ∆/3 + 1 is ∆ + 1. This improves results by Meeks and Scott.

The guided modes lying in the upper gap-edge band in the photonic band structure of photonic crystals have negative values of refractive index. This feature generates many interesting optical phenomena, and some spectacular photonic devices such as focusing slabs have been developed. We report the design of a photonic-crystal, planoconcave lens for focusing incident parallel light, and theoreti...