Minimum Number of Palettes in Edge Colorings
نویسندگان
چکیده
منابع مشابه
Minimum sum edge colorings of multicycles
In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assigned to the edges is minimum. The chromatic edge strength of a graph is the minimum number of colors required in a minimum sum edge coloring of this graph. We study the case of multicycles, defined as cycles with paralle...
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Let F (n; k) denote the maximum number of two edge colorings of a graph on n vertices that admit no monochromatic K k , (a complete graph on k vertices). The following results are proved: F (n; 3) = 2 bn 2 =4c for all n 6. F (n; k) = 2 (k?2 2k?2 +o(1))n 2. In particular, the rst result solves a conjecture of Erdd os and Rothschild.
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For a bipartite graph G = (V,E), an edge coloring of G is a coloring of the edges of G such that any two adjacent edges are colored in different colors. In this paper, we consider the problem of enumerating all edge colorings with the fewest number of colors. We propose a simple polynomial delay algorithm whose amortized time complexity is O(|V |) per output, whereas the previous fastest algori...
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In this paper we present a short algebraic proof for a generalization of a formula of R. Penrose, Some applications of negative dimensional tensors, in: Combinatorial Mathematics and its Applications Welsh (ed.), Academic Press, 1971, pp. 221–244 on the number of 3-edge colorings of a plane cubic graph. We also show that the number of 3-edge colorings of cubic graphs can be computed (up to a fa...
متن کاملThe number of edge colorings with no monochromatic triangle
Let F (n, k) denote the maximum number of two edge colorings of a graph on n vertices that admit no monochromatic Kk, (a complete graph on k vertices). The following results are proved: F (n, 3) = 2bn /4c for all n ≥ 6. F (n, k) = 2 k−2 2k−2+o(1))n 2 . In particular, the first result solves a conjecture of Erdös and Rothschild.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2013
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-013-1298-8