On a total version of 1-2-3 Conjecture
نویسندگان
چکیده
منابع مشابه
An oriented version of the 1-2-3 Conjecture
The well-known 1-2-3 Conjecture addressed by Karoński, Luczak and Thomason asks whether the edges of every undirected graph G with no isolated edge can be assigned weights from {1, 2, 3} so that the sum of incident weights at each vertex yields a proper vertex-colouring of G. In this work, we consider a similar problem for oriented graphs. We show that the arcs of every oriented graph − → G can...
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A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper we show that such a weighting is possible from the weight set {1, 2, . . . , r + 1} for all linear hypergraphs with maximum edge size r ≥ 4 and not containin...
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The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configur...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2020
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2223