非极大部分对偶平面图的刻画与平面三角剖分图的部分对偶最大亏格  

A Characterization Theorem for Nonmaximal Partial-dual Planar Graphs and the Maximum Partial-dual Genus for a Planar Triangulated Graph

作　　者：秦楚 陈仪朝 Chu QIN;Yi Chao CHEN(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,P.R.China)

机构地区：[1]苏州科技大学数学科学学院,苏州215009

出　　处：《数学学报（中文版）》2024年第3期531-538,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12271392);江苏省研究生科研创新计划项目(KYCX21_3001)。

摘　　要：图嵌入G的部分对偶G^(A)是选择G的部分边集A做对偶,它是经典的庞加莱对偶G^(*)的推广.与经典的庞加莱对偶不同的是,部分对偶G^(A)的亏格往往不等于G的亏格.类似于黄-刘图的非上可嵌入性刻画定理,对平面图我们先证明了非极大部分对偶平面图结构定理,并由此确定了平面三角剖分图G的部分对偶最大亏格,即当G为3-圈时,G的部分对偶最大亏格为1;否则G的部分对偶最大亏格为其顶点数减1.The partial duality G^(A)of an embedded graph G can be seen as geometric duality over a partial edge set A of G.It is a generalization of the classic Poincare duality G^(*).Unlike the classic Poincaréduality,the genus of G^(A)is often not equal to the genus of G.Similar to the Huang-Liu's characterization theorem of non upperembedability of graphs,we first prove a structure theorem for nonmaximal partial-dual planar graphs.Then,we determine the maximum partial-dual genus for a planar triangulated graph G,that is,if G is 3-cycle,the maximum partial-dual genus of G is1;Otherwise the maximum partial-dual genus of G is equal to the number of vertices minus 1.

关 键 词：部分对偶 极大部分对偶平面图 平面三角剖分图 部分对偶最大亏格 

分 类 号：O157.5[理学—数学]