منابع مشابه
Characterization of Uniquely Colorable and Perfect Graphs
This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The main results are 1) Every uniquely k-colorable graph is (k 1)-connected. 2) If G is a uniquely k-colorable graph, then (G) ≥ k l. 3) A maximal planar graph G of order 3 or more has chromatic number 3 if and only if G is Eulerian. 4) Every interval graph is perfect. 5) A graph G is chordal if and only if G can b...
متن کاملUniquely 2-list colorable graphs
A graph is called to be uniquely list colorable, if it admits a list assignment which induces a unique list coloring. We study uniquely list colorable graphs with a restriction on the number of colors used. In this way we generalize a theorem which characterizes uniquely 2–list colorable graphs. We introduce the uniquely list chromatic number of a graph and make a conjecture about it which is a...
متن کاملOn Uniquely List Colorable Graphs
Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k–list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2–list colorable graphs. Here we state some results which will pave the way in character...
متن کاملOn uniquely 3-colorable planar graphs
A k-chromatic graph G is called uniquely k-colorable if every k-coloring of the vertex set V of G induces the same partition of V into k color classes. There is an innnite class C of uniquely 4-colorable planar graphs obtained from the K 4 by repeatedly inserting new vertices of degree 3 in triangular faces. In this paper we are concerned with the well-known conjecture (see 6]) that every uniqu...
متن کاملSplit-critical and uniquely split-colorable graphs
The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring problem from the point of view of split-coloring, such as criticality and the uniqueness of the minimum split-coloring. We discuss some proper...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90059-6