منابع مشابه
On 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 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 کاملSize of edge-critical uniquely 3-colorable planar graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G − e is not a uniquely k-colorable graph for any edge e ∈ E(G). Mel’nikov and Steinberg [L. S. Mel’nikov, R. Steinberg, One counterexample for two conjectures on three coloring, Discrete Math. 20 (1977) 203-206] as...
متن کاملOn uniquely k-list colorable planar graphs, graphs on surfaces, and regular graphs
A graph G is called uniquely k-list colorable (UkLC) if there exists a list of colors on its vertices, say L = {Sv | v ∈ V (G)}, each of size k, such that there is a unique proper list coloring of G from this list of colors. A graph G is said to have property M(k) if it is not uniquely k-list colorable. Mahmoodian and Mahdian [7] characterized all graphs with property M(2). For k ≥ 3 property M...
متن کاملThe Size of Edge-critical Uniquely 3-Colorable Planar Graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G−e is not a uniquely k-colorable graph for any edge e ∈ E(G). In this paper, we prove that if G is an edge-critical uniquely 3-colorable planar graph, then |E(G)| 6 83 |V (G)| − 17 3 . On the other hand, there exis...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80087-6