Degenerate Crossing Numbers

Expected Crossing Numbers

✍ Bojan Mohar; Tamon Stephen 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 188 KB

Degenerate weighted Stirling numbers

✍ F.T Howard 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 631 KB

We define the degenerate weighted Stifling numbers of the first and second kinds, Sl(n, k, 2t ] 0) and S(n, k, )t ] O). By specializing h and 0 we can obtain the Stirling numbers, the weighted Stifling numbers and the degenerate Stifling numbers. Basic properties of Sl(n, k, h { 0) and S(n, k, ;t I

On stable crossing numbers

✍ Paul C. Kainen; Arthur T. White 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 253 KB

## Abstract Results giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for __G__ = __Q__~__n__~ × __K__~4.4~, cr~__y__(__G__)‐__m__~(__G__) = 4__m__, for 0 ⩽ = __m__ ⩽ 2^__n__^. A generalization is obtained, for cer

New Bounds on Crossing Numbers

✍ Pach, J.; Spencer, J.; Tóth, G. 📂 Article 📅 2000 🏛 Springer 🌐 English ⚖ 141 KB

Bounds for rectilinear crossing numbers

✍ Daniel Bienstock; Nathaniel Dean 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 780 KB

## Abstract A rectilinear drawing of a graph is one where each edge is drawn as a straight‐line segment, and the rectilinear crossing number of a graph is the minimum number of crossings over all rectilinear drawings. We describe, for every integer __k__ ≥ 4, a class of graphs of crossing number __

Crossing numbers of imbalanced graphs

✍ János Pach; József Solymosi; Gábor Tardos 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 103 KB

## Abstract The __crossing number__, cr(__G__), of a graph __G__ is the least number of crossing points in any drawing of __G__ in the plane. According to the Crossing Lemma of M. Ajtai, V. Chvátal, M. Newborn, E. Szemerédi, Theory and Practice of Combinatorics, North‐Holland, Amsterdam, New York,