“Fumbling Along the Boundaries of the Personal”: History and Affect in Elizabeth Bowen’s The Last September

Stasi, Paul

doi:10.1353/elh.2017.0027

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Proportional Choosability1

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2019

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“…We will have that if a graph is proportionally k-choosable, it must be equitably k-colorable. The creation of this notion was facilitated by a question asked by Stasi [21] during a talk given by the second author [16].…”

Section: Proportional Choosabilitymentioning

confidence: 99%

Proportional choosability: A new list analogue of equitable coloring

Kaul

Mudrock

Pelsmajer

et al. 2019

Discrete Mathematics

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In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. In this paper, we motivate and define a new list analogue of equitable coloring called proportional choosability. A k-assignment L for a graph G specifies a list L(v) of k available colors for each vertex v of G. An L-coloring assigns a color to each vertex v from its list L(v). For each color c, let η(c) be the number of vertices v whose listWe show that if a graph G is proportionally k-choosable, then every subgraph of G is also proportionally k-choosable and also G is proportionally (k + 1)-choosable, unlike equitable choosability for which analogous claims would be false. We also show that any graph G is proportionally k-choosable whenever k ≥ ∆(G) + ⌈|V (G)|/2⌉, and we use matching theory to completely characterize the proportional choosability of stars and the disjoint union of cliques.

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Section: Proportional Choosabilitymentioning

confidence: 99%