Nowhere‐Zero Flows on Signed Complete and Complete Bipartite Graphs | Zendy

Máčajová Edita | Zendy; Rollová Edita | Zendy

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Nowhere‐Zero Flows on Signed Complete and Complete Bipartite Graphs

Author(s) -

Máčajová Edita,

Rollová Edita

Publication year - 2015

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21793

Subject(s) - bipartite graph , signed graph , mathematics , combinatorics , zero (linguistics) , conjecture , flow (mathematics) , nowhere dense set , graph , discrete mathematics , computer science , geometry , philosophy , linguistics , set (abstract data type) , programming language

Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow.

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