论文信息 - NZ-flows in strong products of graphs

NZ-flows in strong products of graphs

We prove that the strong product G1t G2 of G1 and G2 is Z3-flow contractible if and only if G1t G2 is not Tt K2, where T is a tree (we call Tt K2 a K4-tree). It follows that G1t G2 admits an NZ 3 -flow unless G1t G2 is a K4 -tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3-flow if G1t G2 is not a K4 -tree, and an NZ 4-flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010

Wilfried Imrich | Iztok Peterin | Simon Špacapan | Cun-Quan Zhang

[1] Cun-Quan Zhang. Integer Flows and Cycle Covers of Graphs , 1997 .

[2] Aygul Mamut,et al. A bound on the chromatic number using the longest odd cycle length , 2007 .

[3] Simon Spacapan. Connectivity of Strong Products of Graphs , 2010, Graphs Comb..

[4] Wilfried Imrich,et al. A theorem on integer flows on cartesian products of graphs , 2003 .

[5] Hong-Jian Lai,et al. Nowhere-zero 3-flows in triangularly connected graphs , 2008, J. Comb. Theory, Ser. B.

[6] Jinlong Shu,et al. Nowhere-zero 3-flows in products of graphs , 2005 .

[7] W. T. Tutte,et al. A Contribution to the Theory of Chromatic Polynomials , 1954, Canadian Journal of Mathematics.

[8] Joan Feigenbaum,et al. Finding the prime factors of strong direct product graphs in polynomial time , 1992, Discret. Math..

[9] W. T. Tutte,et al. On the Imbedding of Linear Graphs in Surfaces , 1949 .