منابع مشابه
A note on uniquely H-colorable graphs
For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.
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 the Uniquely List Colorable Graphs
Let G be a graph with ν vertices, and let S1, S2, . . . , Sν be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely k–list colorable graph. We characterize all uniquely 2–list colorable graphs, and discuss uniquely k–list colorable graphs by introducing some open problems. We also show the connectio...
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 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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1973
ISSN: 0095-8956
DOI: 10.1016/0095-8956(73)90022-1