Let P(G,t) and F(G,t) denote the chromatic and flow polynomials of a graph G. G.D. Birkhoff and D.C. Lewis showed that, if G is a plane near triangulation, then the only zeros of...
We study minimum-cost sensor placement on a bounded 3D sensing field, R, which comprises a number of discrete points that may or may not be grid points. Suppose we have types of se...
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
A minimal k-cycle is a family of sets A0, . . . , Ak−1 for which Ai ∩ Aj = ∅ if and only if i = j or i and j are consecutive modulo k. Let fr(n, k) be the maximum size of a ...
Personal photo books are a popular means of capturing important moments and people have ever created this kind of multimedia presentations. With the advent of digital photography ...