Flows on flow-admissible signed graphs
WebApr 17, 2024 · Recently, Rollová et al proved that every flow-admissible signed cubic graph with two negative edges admits a nowhere-zero 7-flow, and admits a nowhere … WebAug 28, 2024 · In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero $6$-flow. Bouchet himself proved that such signed graphs admit nowhere-zero $216$-flows and Zyka further proved that such signed graphs admit nowhere-zero $30$-flows. In this paper we show that every flow-admissible signed …
Flows on flow-admissible signed graphs
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WebMany basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs. However, signed graphs without long barbells in many … WebBouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we proved that every flow-admissible 3-edge-colorable cubic …
WebNov 3, 2024 · Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we proved that every flow-admissible $3$-edge-colorable cubic signed graph admits a nowhere-zero $10$-flow. This together with the 4-color theorem implies … WebMar 1, 2024 · The flow number of a signed graph (G,Σ) is the smallest positive integer k such that (G,Σ) admits a nowhere-zero integer k-flow. In 1983, Bouchet (JCTB) conjectured that every flow-admissible ...
WebApr 17, 2024 · Recently, Rollová et al proved that every flow-admissible signed cubic graph with two negative edges admits a nowhere-zero 7-flow, and admits a nowhere … WebApr 27, 2024 · This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. In this paper, we generalize some early results by Xu and Zhang (Discrete Math.~299, 2005), Schubert and Steffen (European J. Combin.~48, 2015), and Zhu (J. Combin. Theory Ser. B~112, 2015), and show that, for signed graphs, every …
WebAug 29, 2024 · Many basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs. However, signed graphs without long barbells in many ways behave like unsigned graphs from the point view of flows. In this paper, we study whether some basic properties in Tutte's flow theory remain valid for …
WebA signed graph G is flow-admissible if it admits a k-NZF for some positive integer k. Bouchet [2] characterized all flow-admissible signed graphs as follows. Proposition … chinoin mexikochino in mexicanWebKhelladi verified Bouchet's 6-flow conjecture for flow-admissible 3-edge-connected signed graphs without long barbells. Theorem 1.1(Khelladi [6]). Let (G,\sigma ) be a flow-admissible3-edge-connected signed graph. If (G,\sigma ) contains no long barbells, then it admits a nowhere-zero 6-flow. Lu et al. [9] also showed that every flow-admissible ... chino in californiaWebJul 5, 2013 · Bouchet's conjecture, that every flow-admissible signed graph admits a nowhere-zero 6-flow is equivalent to its restriction on cubic graphs. We prove the conjecture for Kotzig-graphs. We study the flow spectrum of regular graphs. In particular the relation of the flow spectrum and the integer flow spectrum of a graph. We show … granite stone blue frying pansWebAn unsigned graph can also be considered as a signed graph with the all-positivesignature, i.e.E N(G,σ)=∅.Let(G,σ)beasignedgraph. ApathP inGiscalleda subdivided edge ofGifeveryinternalvertexofP isa2-vertex. Thesuppressed graph ofG,denoted by G, is the signed graph obtained from G by replacing each maximal subdivided edge P with a chinoin pharmaceutical mexicoWebA signed graph G is flow-admissible if it admits a k-NZF for some positive integer k. Bouchet [2] characterized all flow-admissible signed graphs as follows. Proposition 2.2. ([2]) A connected signed graph G is flow-admissible if and only if ǫ(G) 6= 1 and there is no cut-edge b such that G −b has a balanced component. chinoin plmWebApr 16, 2024 · This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. In this paper, we generalize some early results by Xu and Zhang (Discrete Math. 299, 2005 ... granite stone blue tv offer