Decompositions into two paths

Zdzisław Skupień

Displaying similar documents to “Decompositions into two paths”

Remarks on Hamiltonian properties of squares of graphs

Günter Schaar (1989)

Archivum Mathematicum

Similarity:

Paths in powers of graph

Elena Wisztová (1980)

Časopis pro pěstování matematiky

Similarity:

Hamiltonian connectedness and a matching in powers of connected graphs

Elena Wisztová (1995)

Mathematica Bohemica

Similarity:

In this paper the following results are proved: 1. Let $P_{n}$ be a path with $n$ vertices, where $n \geq 5$ and $n \neq 7, 8$ . 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 $p \geq 5$ , and let $M$ be a matching in $G$ . Then $G^{5} - M$ is hamiltonian-connected.

On k-Path Pancyclic Graphs

Zhenming Bi, Ping Zhang (2015)

Discussiones Mathematicae Graph Theory

Similarity:

For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic. In this paper, we present sufficient conditions for graphs to be k-path pancyclic. For a graph G of order n ≥ 3, we establish sharp lower bounds in terms of n and k for (a) the minimum degree of G, (b) the minimum degree-sum of nonadjacent vertices of G and (c) the size of G...