%0 Journal Article
%T 几类IC-平面图的退化性<br>Degeneracy of Some Classes of IC-Planar Graphs
%A 田鸿珲
%J Advances in Applied Mathematics
%P 3390-3398
%@ 2324-8009
%D 2021
%I Hans Publishing
%R 10.12677/AAM.2021.1010356
%X 若图G的每一个子图H都有δ(H) ≤ k, 则称G是k-退化的. 根据不含k-圈(k ∈ {3, 5, 6})的平面图是3-退化的, 本文证明了不含k-圈的IC-平面图是4-退化的. 本文还进一步证明了3-圈与4-圈不相邻, 3-圈与5-圈不相邻或4-圈与4-圈不相邻的IC-平面图也是4-退化的. 同时, 本文给出了不含k-圈(k ∈ {3, 4, 5, 6})且4-正则的IC-平面图的例子。<br />
If  every  subgraph  H  of  graph  G has  δ(H)  ≤ k,  then  G is k-degenerate. A planar graph without k-cycles (k ∈ {3, 5, 6}) is 3-degenerate, this paper proves that an IC- planar graph without k-cycles is 4-degenerate. This paper is further proved that the IC-planar graph with 3-cycle not adjacent to 4-cycle, 3-cycle not adjacent to 5-cycle or 4-cycle not adjacent to 4-cycle is also 4-degenerate. And we give an example of 4-regular IC-planar graphs without k-cycles (k ∈ {3, 4, 5, 6}).
%K IC-平面图，退化性，权转移<br>IC-Planar Graph
%K Degeneracy
%K Discharging
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=45912