Cops and Robbers on \(\boldsymbol{P_5}\)-Free Graphs

Chudnovsky, Maria; Norin, Sergey; Seymour, Paul D.; Turcotte, Jérémie

doi:10.1137/23m1549912

SIAM J. Discrete Math.

2024

DOI: 10.1137/23m1549912

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Cops and Robbers on \(\boldsymbol{P_5}\)-Free Graphs

Maria Chudnovsky,

Sergey Norin,

Paul D. Seymour

et al.

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2024

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Improved bounds on the cop number when forbidding a minor

Kenter,

Meger,

Turcotte

2024

Journal of Graph Theory

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Andreae proved that the cop number of connected ‐minor‐free graphs is bounded for every graph . In particular, the cop number is at most if contains no isolated vertex, where . The main result of this paper is an improvement on this bound, which is most significant when is small or sparse, for instance, when can be obtained from another graph by multiple edge subdivisions. Some consequences of this result are improvements on the upper bound for the cop number of ‐minor‐free graphs, ‐minor‐free graphs and linklessly embeddable graphs.

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Improved bounds on the cop number when forbidding a minor

Kenter,

Meger,

Turcotte

2024

Journal of Graph Theory

View full text Add to dashboard Cite

show abstract

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Cops and Robbers on \(\boldsymbol{P_5}\)-Free Graphs

Cited by 1 publication

References 14 publications

Improved bounds on the cop number when forbidding a minor

Improved bounds on the cop number when forbidding a minor

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