×

Neighborhood unions involving distances and panconnectivity. (English) Zbl 1203.05062

Summary: Let \(G\) be a 2-connected simple graph of order \(n\) \((n\geq 5)\) and minimum degree \(\delta\). We prove that if \(|N(u)\cup N(v)|\geq n-\delta+1\) for each pair of vertices \(u, v\) of \(G\) at distance two, then for any two vertices \(x\) and \(y\) of \(G\), there exist \(x\)-\(y\) paths of length from \(d(x,y)\) to \(n-1\) with a few exceptions.

MSC:

05C15 Coloring of graphs and hypergraphs
PDFBibTeX XMLCite