Topic
Uniquely colorable graph
About: Uniquely colorable graph is a research topic. Over the lifetime, 6 publications have been published within this topic receiving 73 citations.
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TL;DR: This paper proves a general decomposition theorem for I"G","k", which allows us to give an algebraic characterization of uniquely k-colorable graphs and gives algorithms for testing unique colorability.
47 citations
TL;DR: It is shown that the graph Un + 1 obtained from the wheel Wn + 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n ⩾ 3 is odd except when n = 6 in which case, the graph W is the only graph having the same chromatic POlynomial as that of U7.
15 citations
TL;DR: Lower bounds of Stahl (for general graphs) and of Bollobas and Thomason (for uniquely colorable, vertex transitive graphs) are proved in a simple, elementary way.
15 citations
01 Jan 2001
TL;DR: In this article, the authors presented a uniquely n-colorable graph with, 3 t n 1 2 -n vertices, and their generalizations, and for each integer, they presented two uniquely, 3t n colorable - ) 1 -n graphs which are chromatically equivalent with vertices.
Abstract: For each integer we present a uniquely n-colorable graph with , 3 t n 1 2 � n vertices, and their generalizations. For each integer we present two uniquely , 3 t n colorable - ) 1 ( � n graphs which are chromatically equivalent with vertices, and with 2 2 � n 3 2 � n vertices, and their generalizations.
TL;DR: A uniquely colorable graph G whose chromatic partition contains atleast one g-set is termed as a g-uniquely-coloring graph as discussed by the authors, and the necessary and sufficient condition for and G* to be g -uniquely colorable whenever G G is g-colorable such that |P | ³ 2, G can be both planar and nonplanar.
Abstract: A uniquely colorable graph G whose chromatic partition contains atleast one g - set is termed as a g - uniquely colorable graph. In this paper, we provide necessary and sufficient condition for and G* to be g - uniquely colorable whenever G g- uniquely colorable and also provide constructive characterization to show that whenever G is g- uniquely colorable such that |P | ³ 2, G can be both planarand non planar.