2019/08/02 by Jeffrey A. Mudrock, Mudrock, Jeffrey A., Max Marsh +3
Computer Science · Mathematics · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1908.01657
openalex publication_date 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \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 ≥ max \χ_ℓ(T), Δ(T)/2 + 2 \ where Δ(T) is the maximum degree of a vertex in T and χ_ℓ(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.