Improved Bounds for the Crossing Number of the Mesh of Trees
نویسندگان
چکیده
Improved bounds for the crossing number of the mesh of trees graph, Mn, are derived. In particular, we derive a new lower bound of 5n log n−44n 80 ‡ which improves on the previous bound of Leighton [11] by a constant factor, and an upper bound of (log n− 10 3 )n 2 + 8n− 20 3 . In addition, we construct drawings of Mn which achieve the upper bound number of crossings. We also prove that the crossing number of M4 is 4.
منابع مشابه
Crossing Number Bounds for the Mesh of Trees
Crossing number bounds for the mesh of trees graph are derived.
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ورودعنوان ژورنال:
- Journal of Interconnection Networks
دوره 4 شماره
صفحات -
تاریخ انتشار 2003