# On k-Path Pancyclic Graphs

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 2, page 271-281
- ISSN: 2083-5892

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topZhenming Bi, and Ping Zhang. "On k-Path Pancyclic Graphs." Discussiones Mathematicae Graph Theory 35.2 (2015): 271-281. <http://eudml.org/doc/271089>.

@article{ZhenmingBi2015,

abstract = {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 such that G is k-path pancyclic},

author = {Zhenming Bi, Ping Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Hamiltonian; panconnected; pancyclic; path Hamiltonian; path pancyclic; Hamiltonian graph; panconnected graph; pancyclic graph; path-Hamiltonian graph; path-pancyclic graph},

language = {eng},

number = {2},

pages = {271-281},

title = {On k-Path Pancyclic Graphs},

url = {http://eudml.org/doc/271089},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Zhenming Bi

AU - Ping Zhang

TI - On k-Path Pancyclic Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 2

SP - 271

EP - 281

AB - 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 such that G is k-path pancyclic

LA - eng

KW - Hamiltonian; panconnected; pancyclic; path Hamiltonian; path pancyclic; Hamiltonian graph; panconnected graph; pancyclic graph; path-Hamiltonian graph; path-pancyclic graph

UR - http://eudml.org/doc/271089

ER -

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