Flows in signed graphs with two negative edges
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43964090" target="_blank" >RIV/49777513:23520/18:43964090 - isvavai.cz</a>
Result on the web
<a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p40" target="_blank" >https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p40</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/4458" target="_blank" >10.37236/4458</a>
Alternative languages
Result language
angličtina
Original language name
Flows in signed graphs with two negative edges
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Combinatorics
ISSN
1077-8926
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
1-18
UT code for WoS article
000440230000006
EID of the result in the Scopus database
2-s2.0-85048345743