caa a22 4500 605461759 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10114-015-3386-6 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3386-6 Heavy cycles in 2-connected triangle-free weighted graphs [Elektronische Daten] [Xue Lv, Pei Wang] A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by d w (v). The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a 2-connected triangle-free weighted graph of even size such that d w (u) + d w (v) ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V (G), then G contains a cycle of weight at least 2d. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Heavy cycles nationallicence triangle-free graphs nationallicence weighted graphs nationallicence Lv Xue Department of Mathematics, Renmin University of China, 100872, Beijing, P. R. China aut Wang Pei Department of Mathematics and Physics, China University of Petroleum, 102249, Beijing, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/10(2015-10-01), 1555-1562 1439-8516 31:10<1555 2015 31 10114 https://doi.org/10.1007/s10114-015-3386-6 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/s10114-015-3386-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lv Xue Department of Mathematics, Renmin University of China, 100872, Beijing, P. R. China aut NATIONALLICENCE 700 1- Wang Pei Department of Mathematics and Physics, China University of Petroleum, 102249, Beijing, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/10(2015-10-01), 1555-1562 1439-8516 31:10<1555 2015 31 10114