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JCT
2007
13 years 8 months ago
2007
Let P(G,t) and F(G,t) denote the chromatic and flow polynomials of a graph G. D.R. Woodall has shown that, if G is a plane triangulation, then the only zeros of P(G,t) in (−∞...
JCT
2007
13 years 8 months ago
2007
In [1] Johnson, Robertson, Seymour and Thomas define the notion of directed tree-width dtw(D) of a directed graph D. They ask whether dtw(D) ≥ k − 1 implies that D has a have...
JCT
2007
13 years 8 months ago
2007
Abstract. We consider lattice walks in the plane starting at the origin, remaining in the first quadrant i, j ≥ 0 and made of West, South and North-East steps. In 1965, Germain ...
JCT
2007
13 years 8 months ago
2007
Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 1 2 1 − (d − 1)−2/(d−2) − (g) n where (g) → 0 as g → ∞,...
JCT
2007
13 years 8 months ago
2007
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...