Název:	Flows in signed graphs with two negative edges
Autoři:	Rollová, Edita Schubert, Michael Steffen, Eckhard
Citace zdrojového dokumentu:	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
Datum vydání:	2018
Nakladatel:	Australian National University
Typ dokumentu:	článek article
URI:	2-s2.0-85048345743 http://hdl.handle.net/11025/47056
ISSN:	1077-8926
Klíčová slova v dalším jazyce:	flows;signed graphs;negative edges
Abstrakt v dalším jazyce:	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.
Práva:	© author
Vyskytuje se v kolekcích:	Články / Articles (KMA) OBD

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