关于混合图H-秩的一个注记

A Note on H-rank of Mixed Graph

关于混合图■的H-秩,李书超等人证明了2m(G)-2c(■)≤rk(G)≤2m(G)+c(G)。本文证明了不存在rk(■)=2m(G)-2c(G)+1的混合图,并且存在无穷多个连通混合图■,满足c(G)=k,rk(■)=2m(G)-2c(G)+l,其中k,l是满足0≤l≤3k,l≠1的整数。

For any mixed graph ■,Li et al. proved that 2 m(G)-2 c(G) ≤rk(■) ≤2 m(G) +c(G). In this paper,we prove that there is no mixed graph ■ with rk(■) =2 m(G)-2 c(G) +1,and there are infinitely many connected mixed graphs ■ such that c(G) =k and rk(G) =2 m(G)-2 c(G) +l for every integers k,l satisfying 0 ≤l ≤3 k, l ≠1.