Chromatic roots at 2 and the Beraha number B10

By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number B10=(5+5)∕2 is a chromatic root. As it was previously known that no other noninteger Beraha...

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Bibliographic Details
Published in:Journal of graph theory 2020-11, Vol.95 (3), p.445-456
Main Authors: Harvey, Daniel J., Royle, Gordon F.
Format: Article
Language:English
Subjects:
Beraha number
chromatic polynomial
chromatic root
Graphs
Polynomials
Questions
recursive family
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Summary:By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number B10=(5+5)∕2 is a chromatic root. As it was previously known that no other noninteger Beraha number is a chromatic root, this completes the determination of precisely which Beraha numbers can be chromatic roots. Next we construct an infinite family of 3‐connected graphs such that for any k≥1, there is a member of the family with q=2 as a chromatic root of multiplicity at least k. The former resolves a question of Salas and Sokal and the latter a question of Dong and Koh.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22566