{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:12:41Z","timestamp":1758823961634,"version":"3.41.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2006,9,4]],"date-time":"2006-09-04T00:00:00Z","timestamp":1157328000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>Let <jats:inline-formula>$P(G,t)$<\/jats:inline-formula> and <jats:inline-formula>$F(G,t)$<\/jats:inline-formula> denote the chromatic and flow polynomials of a graph <jats:inline-formula>$G$<\/jats:inline-formula>. G. D. Birkhoff and D C. Lewis showed that, if <jats:inline-formula>$G$<\/jats:inline-formula> is a plane near-triangulation, then the only zeros of <jats:inline-formula>$P(G,t)$<\/jats:inline-formula> in <jats:inline-formula>$(-\\infty,2]$<\/jats:inline-formula> are 0, 1 and 2. We will extend their theorem by showing that a stronger result to the dual statement holds for both planar and non-planar graphs: if <jats:inline-formula>$G$<\/jats:inline-formula> is a bridge graph with at most one vertex of degree other than three, then the only zeros of <jats:inline-formula>$F(G,t)$<\/jats:inline-formula> in <jats:inline-formula>$(-\\infty,\\alpha]$<\/jats:inline-formula> are 1 and 2, where <jats:inline-formula>$\\alpha\\approx 2.225\\cdots$<\/jats:inline-formula> is the real zero in <jats:inline-formula>$(2,3)$<\/jats:inline-formula> of the polynomial <jats:inline-formula>$t^4-8t^3+22t^2-28t+17$<\/jats:inline-formula>. In addition we construct a sequence of \u2018near-cubic\u2019 graphs whose flow polynomials have zeros converging to <jats:inline-formula>$\\alpha$<\/jats:inline-formula> from above.<\/jats:p>","DOI":"10.1017\/s0963548306007747","type":"journal-article","created":{"date-parts":[[2006,9,4]],"date-time":"2006-09-04T10:58:46Z","timestamp":1157367526000},"page":"85-108","source":"Crossref","is-referenced-by-count":5,"title":["Zero-Free Intervals for Flow Polynomials of Near-Cubic Graphs"],"prefix":"10.1017","volume":"16","author":[{"given":"BILL","family":"JACKSON","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2006,9,4]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548306007747","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T01:14:33Z","timestamp":1750468473000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548306007747\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9,4]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["S0963548306007747"],"URL":"https:\/\/doi.org\/10.1017\/s0963548306007747","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2006,9,4]]}}}