Puzzling and apuzzling graphs

Puzzling and apuzzling graphs

Let G be a graph with chromatic number χ(G) and consider a partition P of G into connected subgraphs. P is a puzzle on G if there is a unique vertex coloring of G using 1, 2, …, χ(G) such that the sums of the numbers assigned to the partition pieces are all the same. P is an apuzzle if there is a un...

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Bibliographic Details
Main Authors: Daphne Gold, James Henle, Cherry Huang, Tia Lyve, Tara Marin, Jasmine Osorio, Mäneka Puligandla, Bayla Weick, Jing Xia, He Yun, Jize Zhang
Format: Article
Language:English
Published: Taylor & Francis Group 2016-04-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
Vertex coloring
Puzzles
Partitions
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860016000049
Description
Summary:Let G be a graph with chromatic number χ(G) and consider a partition P of G into connected subgraphs. P is a puzzle on G if there is a unique vertex coloring of G using 1, 2, …, χ(G) such that the sums of the numbers assigned to the partition pieces are all the same. P is an apuzzle if there is a unique vertex coloring such that the sums are all different. We investigate the concept of puzzling and apuzzling graphs, detailing classes of graphs that are puzzling, apuzzling and neither.
ISSN:0972-8600

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