Planar triangulations with real chromatic roots arbitrarily close to four

Abstract

We exhibit infinite families of planar graphs with real chromatic roots arbitrarily close to 4, thus resolving a long-standing conjecture in the affirmative.

19 pages, uses PGF/TikZ for graphics

References in corpus (5)

• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits
• Chromatic Polynomials, Potts Models and All That
• Chromatic Polynomials for $J(\prod H)I$ Strip Graphs and their Asymptotic Limits
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips

Cited by in corpus (5)

• A Little Statistical Mechanics for the Graph Theorist
• Graph polynomials and their applications I: The Tutte polynomial
• Is the five-flow conjecture almost false?
• Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
• Errata and Addenda to Mathematical Constants