Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp...Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp(f)∩E(C)|>3/4|E(C)|,and showed that the conjecture holds if|E(C)|≤19[Combinatorica,37,1097–1112(2017)].In this paper,we prove that the conjecture holds if|E(C)|≤27.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11871397,12071370 and U1803263)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-083)。
文摘Let G be a bridgeless graph and C be a circuit in G.To find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp(f)∩E(C)|>3/4|E(C)|,and showed that the conjecture holds if|E(C)|≤19[Combinatorica,37,1097–1112(2017)].In this paper,we prove that the conjecture holds if|E(C)|≤27.
