%0 Journal Article %1 woodall97 %A Woodall, D. R. %D 1997 %J Discrete Mathematics %K algebraic.graph.theory chromatic five.color.theorem graph.theory planar polynomial root root-free %N 1–3 %P 141--153 %R 10.1016/S0012-365X(96)00277-4 %T The Largest Real Zero of the Chromatic Polynomial %V 172 %X It is proved that if every subcontraction of a graph G contains a vertex with degree at most k, then the chromatic polynomial of G is positive throughout the interval (k, ∞); Kk+1 shows that this interval is the largest possible. It is conjectured that the largest real zero of the chromatic polynomial of a χ-chromatic planar graph is always less than χ. For χ = 2 and 3, constructions are given for maximal maximally-connected χ-chromatic planar graphs (i.e., 3-connected quadrangulations for χ = 2 and 4-connected triangulations for χ = 3) whose chromatic polynomials have real zeros arbitrarily close to (but less than) χ.

@article{woodall97, abstract = {It is proved that if every subcontraction of a graph G contains a vertex with degree at most k, then the chromatic polynomial of G is positive throughout the interval (k, ∞); Kk+1 shows that this interval is the largest possible. It is conjectured that the largest real zero of the chromatic polynomial of a χ-chromatic planar graph is always less than χ. For χ = 2 and 3, constructions are given for maximal maximally-connected χ-chromatic planar graphs (i.e., 3-connected quadrangulations for χ = 2 and 4-connected triangulations for χ = 3) whose chromatic polynomials have real zeros arbitrarily close to (but less than) χ. }, added-at = {2015-05-12T07:59:05.000+0200}, author = {Woodall, D. R.}, biburl = {https://www.bibsonomy.org/bibtex/2df13028ddb279e3427a15e13526a3fb4/ytyoun}, doi = {10.1016/S0012-365X(96)00277-4}, interhash = {b1c78767ac3cbc9a29c563c2f7f87923}, intrahash = {df13028ddb279e3427a15e13526a3fb4}, issn = {0012-365X}, journal = {Discrete Mathematics }, keywords = {algebraic.graph.theory chromatic five.color.theorem graph.theory planar polynomial root root-free}, number = {1–3}, pages = {141--153}, timestamp = {2016-04-10T12:37:38.000+0200}, title = {The Largest Real Zero of the Chromatic Polynomial }, volume = 172, year = 1997 }