Minimal Pancyclic Graphs

J. C. George1, Alison Marr2, W. D. Wallis3
1Department of Mathematics and Natural Sciences, Gordon College, Barnesville, GA 30204, USA
2Department of Mathematics and Computer Science, Southwestern University, Georgetown, TX 78626, USA
3Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA

Abstract

A pencyclic graph on \( v \) vertices is called pancyclic if it contains cycles of every length from \( 3 \) to \( v \). In this paper we address the question: what is the minimum number of edges in a pancyclic graph? We present a simple analysis using chord patterns.