Title:	Flows in signed graphs with two negative edges
Authors:	Rollová, Edita Schubert, Michael Steffen, Eckhard
Citation:	ROLLOVÁ, E. SCHUBERT, M. STEFFEN, E. Flows in signed graphs with two negative edges. Electronic Journal of Combinatorics, 2018, roč. 25, č. 2, s. 1-18. ISSN: 1077-8926
Issue Date:	2018
Publisher:	Australian National University
Document type:	článek article
URI:	2-s2.0-85048345743 http://hdl.handle.net/11025/47056
ISSN:	1077-8926
Keywords in different language:	flows;signed graphs;negative edges
Abstract in different language:	The presented paper studies the flow number F(G, σ) of flow-admissible signed graphs (G, σ) with two negative edges. We restrict our study to cubic graphs, because for each non-cubic signed graph (G, σ) there is a set of cubic graphs obtained from (G, σ) such that the flow number of (G, σ) does not exceed the flow number of any of the cubic graphs. We prove that F(G, σ) 6 6 if (G, σ) contains a bridge, and F(G, σ) 6 7 in general. We prove better bounds, if there is a cubic graph (H, σH) obtained from (G, σ) which satisfies some additional conditions. In particular, if H is bipartite, then F(G, σ) 6 4 and the bound is tight. If H is 3-edge-colorable or critical or if it has a sufficient cyclic edge-connectivity, then F(G, σ) 6 6. Furthermore, if Tutte’s 5-Flow Conjecture is true, then (G, σ) admits a nowhere-zero 6-flow endowed with some strong properties.
Rights:	© author
Appears in Collections:	Články / Articles (KMA) OBD

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