On List Equitable Total Colorings of the Generalized Theta Graph

Discussiones Mathematicae Graph Theory

Wagstrom Tim¹  Marsh Max¹  Mudrock Jeffrey A.¹ 

[1] Department of Mathematics, College of Lake County, Grayslake, IL 60030;

关键词: graph coloring;    total coloring;    equitable coloring;    list coloring;    equitable choosability;    05c15;   

DOI  :  10.7151/dmgt.2292

来源: DOAJ

【 摘 要 】

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 ∈ V (G), and an equitable L-coloring of G is a proper coloring, f, of G such that f(v) ∈ L(v) for each v ∈ V (G) and each color class of f has size at most ⌈|V (G)|/k⌉. Graph G is equitably k-choosable if G is equitably L-colorable whenever L is a k-assignment for G. 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 ≥ max{xℓ(T ), Δ(T )/2 + 2} where Δ(T ) is the maximum degree of a vertex in T and xℓ(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.

【 授权许可】

Unknown