Graphs with all holes the same length

Abstract

A graph is "$\ell$-holed" if all its induced cycles of length at least four have length exactly $\ell$. We give a complete description of the $\ell$-holed graphs for each $\ell \ge 7$.

References in corpus (2)

• Vertex decomposable graphs and obstructions to shellability
• On recognition algorithms and structure of graphs with restricted induced cycles

Cited by in corpus (2)

• Longest cycles and longest chordless cycles in $2$-connected graphs
• Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-shortest Induced Paths