Facial Nonrepetitive Vertex Coloring of Plane Graphs
نویسندگان
چکیده
منابع مشابه
Edge-coloring Vertex-weightings of Graphs
Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...
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A sequence r1, r2, . . . , r2n such that ri = rn+i for all 1 ≤ i ≤ n, is called a repetition. A sequence S is called non-repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are coloured. A trail is called non-repetitive if the sequence of colours of its edges is non-repetitive. If G is a plane graph, a facial non-repetitive edge-colo...
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A squarefree word is a sequence w of symbols such that there are no strings x, y, and z for which w = xyyz. A nonrepetitive coloring of a graph is an edge coloring in which the sequence of colors along any open path is squarefree. We show that determining whether a graph G has a nonrepetitive k-coloring is Σ p 2 -complete. When we restrict to paths of lengths at most n, the problem becomes NP-c...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2012
ISSN: 0364-9024
DOI: 10.1002/jgt.21695