%0 Journal Article
%T 极小3-连通平面图的构造<br>The Structure of Minimally 3-Connected Planer Graphs
%A 祝誉升
%J Pure Mathematics
%P 272-279
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.155176
%X 设<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi mathvariant='script'>G</mi>
</math>

是由满足以下条件的3-连通平面二部图所组成的图类&#65306;<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi mathvariant='script'>G</mi>
</math>

的一部是3度点的集合&#65292;另外一部是度至少为4的点的集合。本文证明了若<i>G</i>是极小3-连通平面图且<i>G</i>中不存在边<i>e</i>使得<i>G</i>/<i>e</i>或<i>G</i>/<i>e</i>\<i>f</i>是极小3-连通平面图&#65292;则<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>G</mi><mo>&#x2208;</mo><mi mathvariant='script'>G</mi></mrow>
</math>

&#65292;这里<i>f</i>与<i>e</i>相邻于一个3度点。<br>Let <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi mathvariant='script'>G</mi>
</math>

 be a set of minimally 3-connected planer graphs such that every member of <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi mathvariant='script'>G</mi>
</math>

 is a bipartite graph with one parts of vertices of degree three and the other parts of degree at least four. Let <i>G </i>be a minimally 3-connected planar graph. This paper show that if <i>G</i> has no edge <i>e </i>such that either <i>G</i>/<i>e</i> or <i>G</i>/<i>e</i>\<i>f</i> is minimally 3-connected planar graph then <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>G</mi><mo>&#x2208;</mo><mi mathvariant='script'>G</mi></mrow>
</math>

; here e and f are two edges incident to a vertex of degree 3.
%K 极小3-连通平面图&#65292
%K 结构<br>Minimally 3-Connected Planar Graph
%K Structure
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=116185