NIC-平面图中轻风筝的存在性

Existence of Light Kite in NIC-Planar Graphs

将K1,3任意两点连接起来所形成的图形称为风筝.设H是一个连通图,G∧是一个图类,如果对任意的G∈G∧,G包含一个子图K,K同构于图H,且满足maxx∈V(K){d(G)(x)}≤th<∞∑x∈V(K){d(G)(x)}≤tw<∞那么称H为G∧的轻子图.如果H是一个风筝,就称H为轻风筝.利用权转移方法研究了NIC-平面图中轻风筝的存在性,证明了每个最小度至少为5并且最小边度至少为11的NIC-平面图含有一个最大度至多为29的风筝.

The graph formed by connecting any two points in K1,3 is called kite.Let G∧be a family of graphs and let H be a connected graph,such that at least one member of G contains a subgraph K,K isomorphic to H,such that maxx∈V(K){d(G)(x)}≤th<∞∑x∈V(K){d(G)(x)}≤tw<∞H is called a light subgraph of G∧.If H is kite,then H is called light kite.By discharging method,the existence of light Kite in NIC-Planar Graphs is studied.It is proved that every NIC-planar graph with minimum vertex degree at least 5 and minimum edge degree at least 11 contains kite with maximum degree at most 29.