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Let G = (V, E) be a 2-connected plane graph on n vertices with outer face C such that every 2-vertex cut of G contains at least one vertex of C. Let P G (q) denote the chromatic polynomial of G. We show that (−1) n P G (q) > 0 for all 1 < q ≤ 1.2040.... This result is a corollary of a more general result that (−1) n Z G (q, w) > 0 for all 1 < q ≤ 1.2040...,(More)
For any graph G, let W (G) be the set of vertices in G of degrees larger than 3. We show that for any bridgeless graph G, if W (G) is dominated by some component of G − W (G), then F (G, λ) has no roots in (1, 2), where F (G, λ) is the flow polynomial of G. This result generalizes the known result that F (G, λ) has no roots in (1, 2) whenever |W (G)| 2. We(More)
Maintaining good health and a sense of well-being are top priorities for many people today. Both health and well-being are strongly related to diet. The relationship of diet to overall health and the effect of diet on the incidence of certain chronic illnesses, such as heart disease, diabetes and cancer, continue to be active areas of nutrition research.(More)
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