A degree sum condition on hamiltonian cycles in balanced 3-partite graphs

A degree sum condition for longest cycle

A degree sum condition for longest cycles in 3-connected graphs

✍ Tomoki Yamashita 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 110 KB 👁 1 views

## Abstract For a graph __G__, we denote by __d__~__G__~(__x__) and κ(__G__) the degree of a vertex __x__ in __G__ and the connectivity of __G__, respectively. In this article, we show that if __G__ is a 3‐connected graph of order __n__ such that __d__~__G__~(__x__) + __d__~__G__~(__y__) + __d__~__