Flows on flow-admissible signed graphs

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August undefined, 2024

WebNov 3, 2024 · 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 that every flow-admissible ... WebKhelladi 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 ...

Flows on flow-admissible signed graphs (Journal Article)

WebThe concept of integer flows on signed graphs naturally comes from the study of graphs embedded on nonorientable surfaces, where nowhere‐zero flow emerges as the dual … WebAug 1, 2015 · Let t ≥ 1 be an integer and (G, σ) be a flow-admissible signed (2 t + 1)-regular graph. If G does not have a t-factor, then F c ((G, σ)) ≥ 2 + 2 2 t − 1. 5. r-minimal sets. This section studies the structural implications of the existence of a nowhere-zero (2 + 1 t)-flow on a signed (2 t + 1)-regular graph. Hence, it extends the first ... songs with hot in them

Signed Graphs: From Modulo Flows to Integer-Valued Flows

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 … WebAuthors: DeVos, Matt; Li, Jiaao; Lu, You; Luo, Rong; Zhang, Cun-Quan; Zhang, Zhang Award ID(s): 1700218 Publication Date: 2024-05-01 NSF-PAR ID: 10212630 Journal … 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 … songs with house in the title

Flows on signed graphs without long barbells

Flow number of signed Halin graphs - ScienceDirect

WebJul 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 … 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 ... songs with how in the titleWebAbstract. This paper is devoted to a detailed study of nowhere-zero flows on signed eulerian graphs. We generalise the well-known fact about the existence of nowhere-zero 2 2 2 2-flows in eulerian graphs by proving that every signed eulerian graph that admits an integer nowhere-zero flow has a nowhere-zero 4 4 4 4-flow.We also characterise … songs with hug in the title

"WebApr 17, 2024 · Six-flows on almost balanced signed graphs. Xiao Wang, Xiao Wang. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, China ... 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-zero 6-flow if its … " - Flows on flow-admissible signed graphs

Flows on flow-admissible signed graphs

[1307.1562v2] Nowhere-zero flows on signed regular graphs

WebMar 15, 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 signed graph has flow number at most 6. This conjecture remains open for general signed graphs even for signed planar graphs.A Halin graph … WebMay 1, 2024 · Abstract. In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero 6-flow. Bouchet himself proved that such signed …

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WebThe concept of integer flows on signed graphs naturally comes from the study of graphs embedded on nonorientable surfaces, where nowhere‐zero flow emerges as the dual notion to local tension. In 1983, Bouchet [2] proposed the following conjecture. Conjecture 1.2 (Bouchet [2]). Every flow‐admissible signed graph admits a nowhere‐zero 6‐flow. WebSep 1, 2024 · Let (G, σ) be a 2-edge-connected flow-admissible signed graph. In this paper, we prove that (G, ... Bouchet A Nowhere-zero integral flows on a bidirected …

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 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. 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 …

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 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 …

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 …

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 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 this family of … songs with hoping in the titleWebGraphs or signed graphs considered in this paper are ﬁnite and may have multiple edges or loops. For terminology and notations not deﬁned here we follow [1,4,11]. In 1983, … songs with hummingWebThis paper studies the fundamental relations among integer flows, modulo orientations, integer-valued and real-valued circular flows, and monotonicity of flows in signed … small glass measuring cupsWebAug 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 … songs with hosanna in the titleWebMany 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 this family of … songs with houston in the lyricsWebThe presented paper studies the flow number $F(G,sigma)$ of flow-admissible signed graphs $(G,sigma)$ with two negative edges. We restrict our study to cubic g songs with house or home in titleWebApr 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 … songs with hump in the title