Nowhere-zero 3-flows in triangularly connected graphs

DOI10.1016/j.jctb.2008.02.008zbMath1171.05026OpenAlexW2152194798MaRDI QIDQ958692

Chuixiang Zhou, Rui Xu, Hong-Jian Lai, Cun-Quan Zhang, Geng-Hua Fan

Publication date: 8 December 2008

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jctb.2008.02.008

zbMATH Keywords

chordal graphslocally connectednowhere-zero flowssquares of graphs2-sum of graphstriangularly connected

Mathematics Subject Classification ID

Directed graphs (digraphs), tournaments (05C20) Connectivity (05C40)

Related Items (34)

\(Z_3\)-connectivity of claw-free graphs ⋮ Extendability of contractible configurations for nowhere-zero flows and modulo orientations ⋮ Nowhere-zero 3-flows of graphs with independence number two ⋮ Two equivalent properties of \(\mathcal Z_3\)-connectivity ⋮ Group connectivity of bridged graphs ⋮ Spanning triangle-trees and flows of graphs ⋮ Degree sum of 3 independent vertices and \(Z_3\)-connectivity ⋮ A note on \(Z_3\)-connected graphs with degree sum condition ⋮ Realizing degree sequences as \(Z_3\)-connected graphs ⋮ \(Z_3\)-connectivity of wreath product of graphs ⋮ Group connectivity and group colorings of graphs --- a survey ⋮ Nowhere-zero 3-flows in matroid base graph ⋮ An extremal problem on group connectivity of graphs ⋮ A dual version of the brooks group coloring theorem ⋮ Group connectivity in line graphs ⋮ Nowhere-zero flows on signed wheels and signed fans ⋮ Nowhere-zero 3-flows and modulo \(k\)-orientations ⋮ \(Z_3\)-connectivity of 4-edge-connected 2-triangular graphs ⋮ All 4-edge-connected HHD-free graphs are \({\mathbb{Z}}_3\)-connected ⋮ Equivalent versions of group-connectivity theorems and conjectures ⋮ Ore-condition and \(Z_3\)-connectivity ⋮ A note on the inducibility of 4-vertex graphs ⋮ Group chromatic number of Halin graphs ⋮ Pósa-condition and nowhere-zero 3-flows ⋮ Degree sum condition for \(Z_{3}\)-connectivity in graphs ⋮ Nowhere-zero 3-flows and \(Z_{3}\)-connectivity of a family of graphs ⋮ NZ-flows in strong products of graphs ⋮ Degree sum and nowhere-zero 3-flows ⋮ \(Z_3\)-connectivity with independent number 2 ⋮ Nowhere-zero 3-flows of claw-free graphs ⋮ Note on cycle double covers of graphs ⋮ EVERY N₂-LOCALLY CONNECTED CLAW-FREE GRAPH WITH MINIMUM DEGREE AT LEAST 7 IS Z₃-CONNECTED ⋮ Coloring drawings of graphs ⋮ Group connectivity in \(J_3\) line graphs

Cites Work

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• Nowhere-zero \(Z_3\)-flows through \(Z_3\)-connectivity
• Group connectivity of graphs --- a nonhomogeneous analogue of nowhere-zero flow properties
• Grötzsch's 3-color theorem and its counterparts for the torus and the projective plane
• Group connectivity of 3-edge-connected chordal graphs
• Superposition and constructions of graphs without nowhere-zero \(k\)-flows
• An equivalent version of the 3-flow conjecture
• Nowhere-zero 3-flows in squares of graphs
• Nowhere‐zero 3‐flows in locally connected graphs
• Claw‐decompositions and tutte‐orientations
• 25 pretty graph colouring problems

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