- Tytuł:
- On List Equitable Total Colorings of the Generalized Theta Graph
- Autorzy:
-
Mudrock, Jeffrey A.
Marsh, Max
Wagstrom, Tim - Powiązania:
- https://bibliotekanauki.pl/articles/32326107.pdf
- Data publikacji:
- 2021-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph coloring
total coloring
equitable coloring
list coloring
equitable choosability - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1215-1233
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł