STRONG RAINBOW EDGE-COLOURING OF VARIANTS OF CUBIC HALIN GRAPHS
نویسندگان
چکیده
منابع مشابه
Strong edge-coloring for cubic Halin graphs
A strong edge-coloring of a graph G is a function that assigns to each edge a color such that two edges within distance two apart must receive different colors. The minimum number of colors used in a strong edge-coloring is the strong chromatic index of G. Lih and Liu [14] proved that the strong chromatic index of a cubic Halin graph, other than two special graphs, is 6 or 7. It remains an open...
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A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted sχ′(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a plane graph constructed from a tree T without vertice...
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A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte [9] conjectured that every two-edge-connected cubic graph with no Petersen graph minor is three-edge-colourable. With Neil Robertson, two of us showed that this is true in ...
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A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree∆ has a strong edge-colouring with at most 4∆ + 4 colours. We show that 3∆ + 1 colours suffice if the graph has girth 6, and 4∆ colours suffice if ∆ ≥ 7 or the girth is at least 5. In the last part of the paper, we raise some questions ...
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2017
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v112i1.5