ON LIST EQUITABLE TOTAL COLORINGS OF THE GENERALIZED THETA GRAPH

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 is an element of V (G), and an equitable L-coloring of G is a proper coloring, f, of G such that f(v) is an element of L(v) for each v is an element of 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{chi l (T), Delta(T)/2 + 2} where Delta(T) is the maximum degree of a vertex in T and chi 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.