限制度的IC平面图中轻弦4-圈的权和

Weight of Light Chords 4-Cycles in IC-Planar Graphs with Degree Restrictions

删去完全图k 4任意一条边所得的图称为弦4-圈.利用权转移方法讨论限制度的IC-平面图中轻弦4-圈的权和,证明每个最小度至少为5且最小边度至少为11的IC-平面图含有一个轻弦4-圈v 1v 2v 3v 4v 1,并证明具有该类限制度的IC-平面图中轻弦4-圈权和的上界小于等于37.

The graph formed by removing an edge from a complete graph k 4 was called chordal 4-cycle.By discharging method,the author discussed the weight of 4-cycle with chords in IC-planar graphs with degree restrictions.The author proved that each IC-planar graph with minimum vertex degree at least 5 and minimum edge degree at least 11 contained a light chordal 4-cycle v1v2v3v4v1,and proved that the upper bounds of weight of this kind of light chordal 4-cycle was at most 37.