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Hamiltonian connectedness and a matching in powers of connected graphs

Elena Wisztová (1995)

Mathematica Bohemica

In this paper the following results are proved: 1. Let P n be a path with n vertices, where n 5 and n 7 , 8 . Let M be a matching in P n . Then ( P n ) 4 - M is hamiltonian-connected. 2. Let G be a connected graph of order p 5 , and let M be a matching in G . Then G 5 - M is hamiltonian-connected.

Interval edge colorings of some products of graphs

Petros A. Petrosyan (2011)

Discussiones Mathematicae Graph Theory

An edge coloring of a graph G with colors 1,2,...,t is called an interval t-coloring if for each i ∈ {1,2,...,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let ℜ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if G,H ∈ 𝔑, then the Cartesian product of these graphs...

Currently displaying 181 – 200 of 455