# Odd holes in bull-free graphs

## TL;DR

This paper proves that detecting induced odd cycles of length at least five can be done in polynomial time for graphs without a bull subgraph, advancing understanding of graph cycle detection.

## Contribution

It introduces a polynomial-time algorithm for detecting odd holes in bull-free graphs, a problem previously of unknown complexity.

## Key findings

- Polynomial-time detection of odd holes in bull-free graphs
- Characterization of bull-free graphs for cycle detection
- Advancement in graph cycle detection algorithms

## Abstract

The complexity of testing whether a graph contains an induced odd cycle of length at least five is currently unknown. In this paper we show that this can be done in polynomial time if the input graph has no induced subgraph isomorphic to the bull (a triangle with two disjoint pendant edges).