# Uniquely list colorability of the graph Kn2 + Om

## Authors

• Le Xuan Hung HaNoi University for Natural Resources and Environment 41 A, Phu Dien Road, Phu Dien precinct, North Tu Liem district, Hanoi, Vietnam

## Keywords:

Vertex coloring (coloring), list coloring, uniquely list colorable graph, complete r-partite graph

## Abstract

Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper vertex coloring of G where each vertex v takes its color from L(v). The graph is uniquely k-list colorable if there is a list assignment L such that jL(v)j = k for every vertex v and the graph has exactly one L-coloring with these lists. In this paper, we characterize uniquely list colorability of the graph G = Kn2 + Om. We shall prove that if n = 2 then G is uniquely 3-list colorable if and only if m >= 9, if n = 3 and m >=1 then G is uniquely 3-list colorable, if n >=4 then G is uniquely k-list colorable with k =[m/2]+1, and if m>=n-1, entonce G es UnLC.

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2020-07-25

## How to Cite

Xuan Hung, L. (2020). Uniquely list colorability of the graph Kn2 + Om. Selecciones Matemáticas, 7(01), 25-28. https://doi.org/10.17268/sel.mat.2020.01.03

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