منابع مشابه
Every 4-regular graph is acyclically edge-6-colorable
An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a(G) of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiamčik (1978) and later Alon, Sudakov and Zaks (2001) conjectured that a(G) ≤ ∆ + 2 for any simple graph G with maximum degree ∆. Basavaraju and Chandran (2009) show...
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We show that a 6-regular graph of diameter d embedded on the torus can have at most 3d + 3d+ 1 vertices having exhibited a graph of this order for each d ≥ 1. 1 6-regular Toroidal Graphs In [1] it is proven that all 6-regular toroidal graphs can have their vertices arranged in a rectangular based grid structure with parallel diagonals across every sub-rectangle in the grid. A special case of th...
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A graph G is called uniquely k-list colorable (UkLC) if there exists a list of colors on its vertices, say L = {Sv | v ∈ V (G)}, each of size k, such that there is a unique proper list coloring of G from this list of colors. A graph G is said to have property M(k) if it is not uniquely k-list colorable. Mahmoodian and Mahdian [7] characterized all graphs with property M(2). For k ≥ 3 property M...
متن کاملMinimum Tenacity of Toroidal graphs
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(03)00242-5