Cops and Robbers on Graphs Based on Designs

We investigate the cop number of graphs based on combinatorial designs. Incidence graphs, point graphs, and block intersection graphs are studied, with an emphasis on finding families of graphs with large cop number. We generalize known results on Meyniel extremal families by supplying bounds on the...

Full description

Saved in:
Bibliographic Details
Published inJournal of combinatorial designs Vol. 21; no. 9; pp. 404 - 418
Main Authors Bonato, Anthony, Burgess, Andrea
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.09.2013
Wiley Subscription Services, Inc
Subjects
05C51
05C57
block intersection graphs
cop number
Cops and Robbers
G-designs
Graphs
group divisible designs
incidence graphs
partial geometries1991 Mathematics Subject Classification. 05B05
partial geometries1991 Mathematics Subject Classification. 05B05, 05C57, 05C51
point graphs
polarity graphs
projective planes
Studies
Online AccessGet full text
ISSN1063-8539
1520-6610
DOI10.1002/jcd.21331

Cover

More Information
Summary:We investigate the cop number of graphs based on combinatorial designs. Incidence graphs, point graphs, and block intersection graphs are studied, with an emphasis on finding families of graphs with large cop number. We generalize known results on Meyniel extremal families by supplying bounds on the incidence graphs of transversal designs, certain G‐designs, and BIBDs with λ≥1. Families of graphs with diameter 2, C4‐free, and with unbounded chromatic number are described with the conjectured asymptotically maximum cop number.
Bibliography:NSERC
Ryerson
ArticleID:JCD21331
istex:A104DC7F799EDF28556AC19154602F33E0B1B300
Mprime
ark:/67375/WNG-R8R4HJFL-6
Contract grant sponsors: NSERC, Mprime, and Ryerson.
ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.21331