The maximum number of diagonals of a cycle in a block (Q1069958)

Let \(C=v_ 1v_ 2\ldots v_ mv_ 1\) be a cycle in a graph. An edge \(v_ iv_ j\) is called a diagonal of C if \(i\not\in \{j-1,j+1\}\). In this note the author proves that if G is a 2-connected graph having minimum degree n and at least 2n vertices then there exists a cycle in G with at least n(n-2) diagonals. The result is concerned with a conjecture proposed by \textit{R. P. Gupta, J. Kahn} and \textit{N. Robertson} [Discrete Math. 32, 37-43 (1980; Zbl 0468.05047)].