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- W4288274833 abstract "In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A $k$-assignment, $L$, for a graph $G$ assigns a list, $L(v)$, of $k$ available colors to each $v in V(G)$, and an equitable $L$-coloring of $G$ is a proper coloring, $f$, of $G$ such that $f(v) in L(v)$ for each $v in V(G)$ and each color class of $f$ has size at most $lceil |V(G)|/k rceil$. In 2018, Kaul, Mudrock, and Pelsmajer subsequently introduced the List Equitable Total Coloring Conjecture which states that if $T$ is a total graph of some simple graph, then $T$ is equitably $k$-choosable for each $k geq max {chi_ell(T), Delta(T)/2 + 2 }$ where $Delta(T)$ is the maximum degree of a vertex in $T$ and $chi_ell(T)$ is the list chromatic number of $T$. In this paper we verify the List Equitable Total Coloring Conjecture for subdivisions of stars and the generalized theta graph." @default.
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- W4288274833 date "2019-08-01" @default.
- W4288274833 modified "2023-09-27" @default.
- W4288274833 title "On List Equitable Total Colorings of the Generalized Theta Graph" @default.
- W4288274833 doi "https://doi.org/10.48550/arxiv.1908.01657" @default.
- W4288274833 hasPublicationYear "2019" @default.
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