On uniquely colorable graphs without short cycles
نویسندگان
چکیده
منابع مشابه
On 3-colorable planar graphs without short cycles
Let G be a graph. It was proved that if G is a planar graph without {4, 6, 7}-cycles and without two 5-cycles sharing exactly one edge, then G 3-colorable. We observed that the proof of this result is not correct. 1 Let G be a simple graph with vertex set G. A planar graph is one that can be drawn on a plane in such a way that there are no “edge crossings,” i.e. edges intersect only at their co...
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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...
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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 کاملA 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.
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1973
ISSN: 0528-2195
DOI: 10.21136/cpm.1973.108481