1. bookAHEAD OF PRINT
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

Chorded k-Pancyclic and Weakly k-Pancyclic Graphs

Published Online: 18 Feb 2022
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 27 Sep 2021
Accepted: 10 Jan 2022
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
Abstract

As natural relaxations of pancyclic graphs, we say a graph G is kpancyclic if G contains cycles of each length from k to |V (G)| and G is weakly pancyclic if it contains cycles of all lengths from the girth to the circumference of G, while G is weakly k-pancyclic if it contains cycles of all lengths from k to the circumference of G. A cycle C is chorded if there is an edge between two vertices of the cycle that is not an edge of the cycle. Combining these ideas, a graph is chorded pancyclic if it contains chorded cycles of each length from 4 to the circumference of the graph, while G is chorded k-pancyclic if there is a chorded cycle of each length from k to |V (G)|. Further, G is chorded weakly k-pancyclic if there is a chorded cycle of each length from k to the circumference of the graph. We consider conditions for graphs to be chorded weakly k-pancyclic and chorded k-pancyclic.

Keywords

MSC 2010

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