On Light Graphs in 3-Connected Plane Graphs Without Triangular or Quadrangular Faces

On 3-Connected Plane Graphs without Tria

On 3-Connected Plane Graphs without Triangular Faces

✍ J. Harant; S. Jendrol'; M. Tkác 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 151 KB

We prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold M with Euler characteristic /(M) contains a k-path, i.e., a path on k vertices, such that each vertex of this path has, in G, degree at most (5Â2) k if M is a sphere S 0 and at most (kÂ2)w(5+-49&24/(M))Â2x i