On the degrees of vertices in locally finite graphs which possess a certain edge deletion property

A remark on the number of vertices of de

A remark on the number of vertices of degree k in a minimally k-edge-connected graph

✍ Mao-cheng Cai 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 395 KB

Let G be a minimally k-edge-connected simple graph and u\*(G) be the number of vertices of degree k in G. proved that (i) uk(G) 2 l(jGl -1)/(2k + l)] + k + 1 for even k, and (ii) uI(G) 2 [lGl/(k + l)] + k for odd k 35 and u,(G) 2 lZlGl/(k + l)] + k -2 for odd k 27, where ICI denotes the number of v