不含4至7-圈且不含相交三角形的平面图的(I, F)-分解
(I, F)-Partition of Planar Graphs Having Neither Cycles of Lengths from 4 to 7 nor Intersecting Triangles
DOI: 10.12677/aam.2026.156278, PDF,    科研立项经费支持
作者: 亢莹利：金华职业技术大学公共基础学院，浙江 金华
关键词: 平面图；(I； F)-分解；超延拓；权转移；Planar Graphs； (I； F)-Partition； Super-Extension； Discharging
摘要: 若一个图G的顶点集可划分为两个部分，其中一个部分为独立集而另一部分的诱导子图为森林，则称G是(I, F)-可分解的。本文证明了任意不含4至7-圈且不含相交三角形的平面图是(I, F)-可分解的。
Abstract: A graph is (I, F)-partitionable if its vertex set can be divided into two subsets such that one is an independent set and the other induces a forest. This paper proves that every planar graph having neither cycles of lengths from 4 to 7 nor intersecting triangles is (I, F)-partitionable.
文章引用：亢莹利. 不含4至7-圈且不含相交三角形的平面图的(I, F)-分解[J]. 应用数学进展, 2026, 15(6): 204-209. https://doi.org/10.12677/aam.2026.156278

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