（v_3）组态的约化

Forbidden Families of Minimal Quadratic and Cubic Configurations

A matrix is \emph{simple} if it is a (0,1)-matrix and there are no repeated columns. Given a (0,1)-matrix $F$, we say a matrix $A$ has $F$ as a \emph{configuration}, denoted $F\prec A$, if there is a submatrix of $A$ which is a row and column permutation of $F$. Let $|A|$ denote the number of columns of $A$. Let $\mathcal{F}$ be a family of matrices. We define the extremal function $\text{forb}(m, \mathcal{F}) = \max\{|A|\colon A \text{ is an }m-\text{rowed simple matrix and has no configuration } F\in\mathcal{F}\}$. We consider pairs $\mathcal{F}=\{F_1,F_2\}$ such that $F_1$ and $F_2$ have no…

On the configurations of nine points on a cubic curve

We study the reciprocal position of nine points in the plane, according to their collinearities. In particular, we consider the case in which the nine points are contained in an irreducible cubic curve and we give their classification. If we consider two configurations different when the associated incidence structures are not isomorphic, we see that there are 131 configurations that can be realized in $\mathbb{P}^2_{\mathbb{Q}}$, and there are two more in $\mathbb{P}^2_K$, where $K =\mathbb{Q}[\sqrt{-3}]$ (one of the two is the Hesse configuration given by the nine inflection points of a cubi…

不可约伪2-因子同构三次二部图

Irreducible pseudo 2-factor isomorphic cubic bipartite graphs

一个二部图是{ \em伪2-因子同构}的，如果它的所有2-因子具有相同的圈数奇偶性.在\cite{ADJLS}中，我们证明了围长为4的本质4-边连通伪2-因子同构三次二部图是$K_{3,3}$，并证明了\cite [猜想3.6]{ADJLS}中本质4-边连通三次二部图是$K_{3,3}$、Heawood图和Pappus图.由于Martinetti（1886），所有对称构型$n_3$都可以从一组无限的所谓的{ \em不可约}构型\cite{VM}中得到，所以存在对称构型$n_3$的一个特征. Boben \cite{B}用它们的{ \em不可约Levi图}完成了不可约构形的列表.本文刻画了不可约伪2-因子同构立方二部图，证明了伪2-因子同构不可约Levi图只有Heawood图和Pappus图。此外，所得到的表征允许我们部分地证明上述猜想。