×

Nowhere-zero flows in Cartesian bundles of graphs. (English) Zbl 1293.05325

Summary: We extend the results of W. Imrich and R. Škrekovski [J. Graph Theory 43, No.2, 93-98 (2003; Zbl 1019.05058)] concerning nowhere-zero flows in Cartesian product graphs to ’twisted’ Cartesian products, that is, Cartesian bundles. Our main result states that every Cartesian bundle of two graphs without isolated vertices has a nowhere-zero 4-flow.

MSC:

05C76 Graph operations (line graphs, products, etc.)
05C21 Flows in graphs

Citations:

Zbl 1019.05058
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Diestel, R., Graph Theory (2005), Springer: Springer Heidelberg · Zbl 1074.05001
[2] Gross, J. L.; Tucker, T. W., Topological Graph Theory (1987), Wiley-Interscience: Wiley-Interscience New York · Zbl 0621.05013
[3] Imrich, W.; Pisanski, T.; Žerovnik, J., Recognizing Cartesian graph bundles, Discrete Math., 167-168, 393-403 (1997) · Zbl 0876.05094
[4] Imrich, W.; Škrekovski, R., A theorem on integer flows on Cartesian products of graphs, J. Graph Theory, 43, 93-98 (2003) · Zbl 1019.05058
[5] Jaeger, F., Nowhere-zero flow problems, (Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory, Vol. 3 (1988), Academic Press: Academic Press London), 71-95 · Zbl 0658.05034
[6] Klavžar, S.; Mohar, B., The chromatic numbers of graph bundles over cycles, Discrete Math., 138, 301-314 (1995) · Zbl 0818.05035
[7] Kwak, J. H.; Lee, J., Isomorphism classes of graph bundles, Canad. J. Math., 42, 747-761 (1990) · Zbl 0739.05042
[8] Mohar, B.; Pisanski, T.; Škoviera, M., The maximum genus of graph bundles, European J. Combin., 9, 215-224 (1988) · Zbl 0642.05019
[9] Pisanski, T.; Vrabec, J., Graph bundles, Preprint Ser. Dep. Math. Univ. Ljubljana, 20, 079, 213-298 (1982)
[10] Shu, J.; Zhang, C.-Q., Nowhere-zero 3-flows in products of graphs, J. Graph Theory, 50, 79-89 (2005) · Zbl 1069.05040
[11] Zhang, C.-Q., Integer Flows and Cycle Covers of Graphs (1997), Dekker: Dekker New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.