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 … 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 …

Six‐flows on almost balanced signed graphs Request PDF

WebThis paper studies the fundamental relations among integer flows, modulo orientations, integer-valued and real-valued circular flows, and monotonicity of flows in signed … WebGraphs 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, … irm chpo bourgoin

Flows on Signed Graphs without Long Barbells

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 ... 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 … WebGraphs 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, … irm chpl