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On the imaginary parts of chromatic roots
Author(s) -
Brown Jason I.,
Wagner David G.
Publication year - 2020
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22487
Subject(s) - mathematics , chromatic scale , the imaginary , combinatorics , graph , order (exchange) , discrete mathematics , psychology , finance , economics , psychotherapist
While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order n (ie, with n vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed p ∈ ( 0 , 1 ) , almost every random graph G in the Erdös‐Rényi model has a nonreal root.