caa a22 4500 47577809X CHVBK 20180406123636.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00007224 doi (NATIONALLICENCE)springer-10.1007/PL00007224 Li Hao Laboratoire de Recherche en Informatique, URA 410, C.N.R.S. Bât. 490, Université de Paris-sud, 91405-Orsay cedex, France. e-mail: li@lri.fr, FR aut On Cycles in 3-Connected Graphs [Elektronische Daten] [Hao Li] Abstract.:  Let G be a 3-connected graph of order n and S a subset of vertices. Denote by δ(S) the minimum degree (in G) of vertices of S. Then we prove that the circumference of G is at least min{|S|, 2δ(S)} if the degree sum of any four independent vertices of S is at least n+6. A cycle C is called S-maximum if there is no cycle C ′ with |C ′∩S|>|C∩S|. We also show that if ∑4 i=1 d(a i)≥n+3+|⋂4 i=1 N(a i)| for any four independent vertices a 1, a 2, a 3, a 4 in S, then G has an S-weak-dominating S-maximum cycle C, i.e. an S-maximum cycle such that every component in G−C contains at most one vertex in S. Springer-Verlag Tokyo, 2000 https://doi.org/10.1007/PL00007224 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00007224 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Li Hao Laboratoire de Recherche en Informatique, URA 410, C.N.R.S. Bât. 490, Université de Paris-sud, 91405-Orsay cedex, France. e-mail: li@lri.fr, FR aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer