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On graphs having no chromatic zeros in (1, 2)
Citation
Dong, F. M., & Koh, K. M. (2006). On graphs having no chromatic zeros in (1, 2). SIAM Journal on Discrete Mathematics, 20(3), 799-810. https://doi.org/10.1137/04061787X
Abstract
For a graph G of order n ≥ 2, an ordering (x1, x2, . . . , xn) of the vertices in G is called a double-link ordering of G if x1x2 ∈ E(G) and xi has at least two neighbors in {x1, x2, . . . , xi−1} for all i = 3, 4, . . . , n. This paper shows that certain graphs possessing a kind of double-link ordering have no chromatic zeros in the interval (1, 2). This result implies that all graphs with a 2-tree as a spanning subgraph, certain graphs with a Hamiltonian path, all complete t-partite graphs, where t ≥ 3, and all (v(G) − Δ(G) + 1)-connected graphs G have no chromatic zeros in the interval (1, 2).
Date Issued
2006
Publisher
Society for Industrial and Applied Mathematics
Journal
SIAM Journal on Discrete Mathematics