caa a22 4500 605460957 CHVBK 20210128100241.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10114-015-3452-0 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3452-0 Li Zhao Department of Mathematics, Minzu University of China, 100081, Beijing, P. R. China aut The cycle structure for directed graphs on surfaces [Elektronische Daten] [Zhao Li] In this paper, the cycle structures for directed graphs on surfaces are studied. If G is a strongly connected graph, C is a Π-contractible directed cycle of G, then both of Int(C,Π) and Ext(C,Π) are strongly connected graph; the dimension of cycles space of G is identified. If G is a strongly connected graph, then the structure of MCB in G is unique. Let G be a strongly connected graph, if G has been embedded in orientable surface S g with f w (G) ≥ 2 (f w (G) is the face-width of G), then any cycle base of G must contain at least 2g noncontractible directed cycles; if G has been embedded in non-orientable surface N g , then any cycle base of G must contain at least g noncontractible directed cycles. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2014 Directed graph nationallicence strongly connected nationallicence directed cycles nationallicence cycles space nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 170-176 1439-8516 31:1<170 2015 31 10114 https://doi.org/10.1007/s10114-015-3452-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3452-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Li Zhao Department of Mathematics, Minzu University of China, 100081, Beijing, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 170-176 1439-8516 31:1<170 2015 31 10114