2015/10/01 by Thomas Perrett, Perrett, Thomas
Computer Science · Mathematics · #05C31 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1510.00417
openalex publication_date 2015/10/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
It is proved that if G is a graph containing a spanning tree with at most\nthree leaves, then the chromatic polynomial of G has no roots in the interval\n(1,t1], where t1 \≈ 1.2904 is the smallest real root of the\npolynomial (t-2)6 +4(t-1)2(t-2)3 -(t-1)4. We also construct a family of\ngraphs containing such spanning trees with chromatic roots converging to t1\nfrom above. We employ the Whitney 2-switch operation to manage the analysis\nof an infinite class of chromatic polynomials.\n