The base graph of a simple matroid M = （E, A） is the graph G such that V（G） = A and E（G） = {BB＇： B, B＇ B, [B ／ B＇｜ = 1}, where the same notation is used for the vertices of G and the bases of M. It is prov...The base graph of a simple matroid M = （E, A） is the graph G such that V（G） = A and E（G） = {BB＇： B, B＇ B, [B ／ B＇｜ = 1}, where the same notation is used for the vertices of G and the bases of M. It is proved that the base graph G of connected simple matroid M is Z3-connected if ｜V（G）｜ ≥5. We also proved that if M is not a connected simple matroid, then the base graph G of M does not admit a nowhere-zero 3-flow if and only if IV（G）[ =4. Furthermore, if for every connected component Ei （ i≥ 2） of M, the matroid base graph Gi of Mi=MIEi has IV（Gi）｜≥5, then G is Z3-connected which also implies that G admits nowhere-zero 3-flow immediately.展开更多
文摘The base graph of a simple matroid M = （E, A） is the graph G such that V（G） = A and E（G） = {BB＇： B, B＇ B, [B ／ B＇｜ = 1}, where the same notation is used for the vertices of G and the bases of M. It is proved that the base graph G of connected simple matroid M is Z3-connected if ｜V（G）｜ ≥5. We also proved that if M is not a connected simple matroid, then the base graph G of M does not admit a nowhere-zero 3-flow if and only if IV（G）[ =4. Furthermore, if for every connected component Ei （ i≥ 2） of M, the matroid base graph Gi of Mi=MIEi has IV（Gi）｜≥5, then G is Z3-connected which also implies that G admits nowhere-zero 3-flow immediately.
