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APPLICATIONS OF matroid PARTITION TO TREE DECOMPOSITION

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 199-204页

作者：蔡茂诚袁旭东 Institute of Systems Science the Chinese Academy of Sciences Beijing China

In this paper we present a matroid approach to the tree decomposition problem, give alternative proofs of the main results in [1,2], which give the necessary and sufficient conditions for a graph C=(V,E) of order n to have a tree decomposition (T_1,T_2): (i) Ti is of order n-1 and excludes the specified vertex ui V, i=1,2; (n) TI is a spanning tree, T_2 is of order n-2 and excludes the specified vertices u_l,u_2∈V. As an application, we give a necessary and sufficient condition for a connected graph to have a tree-decomposition of {n-1,n-1}.

关键词： Thee graph matroid partition decomposition

PROOF OF A CONJECTURE ON matroid BASE GRAPHS

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Science China Mathematics 1990年第11期33卷 1329-1337页

作者：刘桂真 Department of Mathematics Shandong University Jinan 250100 PRC

Let G be the base graph of a matroid. L et k(G),λ(G) and δ(G)denote the connectivity edge-connectivity and the minimum degree of G, respectively. The conjecture that k(G)= λ(G)=δ(G) is proved true for any matroid.

关键词： matroid base graph connectivity.

NEW APPROACHES TO THE GRAPHICNESS OF A matroid

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Systems Science and Mathematical Sciences 1999年第S1期12卷 31-42页

作者： LIU Yanpei(Institute of Mathematics, Northern Jiaotong University, Beijing 100044 China)

This article provides some new characterizations for testing if a matroid isgraphic. One of them can be seen as a consequence deduced from the Wu’s theory on theplanarity of graphs.

关键词： matroid graphicness basic order.

The Facets of the Bases Polytope of a matroid and Two Consequences

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Open Journal of Discrete Mathematics 2018年第1期8卷 14-20页

作者： Brahim Chaourar Department of Mathematics and Statistics Al Imam Mohamed Ibn Saud University (IMSIU) Riyadh Saudi Arabia

Let M be a matroid defined on a finite set E and L?⊂?E?. L is locked in M if??and ?are 2-connected, and . In this paper, we prove that the nontrivial facets of the bases polytope of M are described by the locked subsets. We deduce that finding the maximum-weight basis of M is a polynomial time problem for matroids with a polynomial number of locked subsets. This class of matroids is closed under 2-sums and contains the class of uniform matroids, the Vámos matroid and all the excluded minors of 2-sums of uniform matroids. We deduce also a matroid oracle for testing uniformity of matroids after one call of this oracle.

关键词： Bases Polytope Facets Locked Subsets Maximum-Weight Basis Problem Polynomially Locked matroids matroid Oracle Testing Unformity of a matroid

matroid与Antimatroid交的两个结果

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重庆交通大学学报(自然科学版) 1988年第2期 6-9页

作者：池洁

本文讨论在一般情况下,matroid与antimatroid交的性质:(E,μ∩(?))系统的秩函数性质和赋权(E,μ∩(?))系统的对偶性质。

关键词：拟阵增广对偶秩函数赋权 Antimatroid matroid 等式

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关于matroid的一个猜测

内蒙古大学学报(自然科学版) 1985年第3期 321-326页

作者：赵萃魁内蒙古大学数学系

1 预备设M是一个秩为r的有限的matroid。用V_k表示M的秩为k的闭集的个数,I_k表示M的k元无关集的个数。Rota猜测数列{W_k}是单峰的。Mason在[4]中指出了更强的猜测:

关键词：个数引理子块 matroid

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关于matroid的一个特征性质

湖北师范学院学报（自然科学版） 1993年第6期16卷 39-41页

作者：左可正

本文给出了 matroid 的一个特征性质,即给出了以下定理:设 S 是集合, 2,Φ∈, 为子集闭的,则（S,）为 matroid 当且仅当下列条件满足:对X={x1,x2…xn)∈,Y={y1,y2,…ym)∈,X、Y 在 F中极大,则 n=m,且适当调整 xi的顺... 详细信息

本文给出了 matroid 的一个特征性质,即给出了以下定理:设 S 是集合, 2,Φ∈, 为子集闭的,则（S,）为 matroid 当且仅当下列条件满足:对X={x1,x2…xn)∈,Y={y1,y2,…ym)∈,X、Y 在 F中极大,则 n=m,且适当调整 xi的顺序,可使i,{y1…yi-1,xi,yi+1…,ym}∈（i=1,2,…n）

关键词： matroid 秩闭包二部图匹配

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关于matroid的一个特征性质

湖北师范大学学报(哲学社会科学版) 1993年第6期 39-41页

作者：左可正

本文给出了matroid的一个特征性质,即给出了以下定理:设S是集合,2;,φ∈为子集闭的,则（S,）为matroid当且仅当下列条件满足:对X={x;,x;,…x;}∈,Y={y;,y;,…y;}∈,X、Y在中极大,则n=m,且适当调整x;的顺序,可使i,{y;…y;,X;,y;,…,y;}∈... 详细信息

本文给出了matroid的一个特征性质,即给出了以下定理:设S是集合,2;,φ∈为子集闭的,则（S,）为matroid当且仅当下列条件满足:对X={x;,x;,…x;}∈,Y={y;,y;,…y;}∈,X、Y在中极大,则n=m,且适当调整x;的顺序,可使i,{y;…y;,X;,y;,…,y;}∈（i=1,2,…n）

关键词： matroid 秩闭包二部图匹配

Eulerian and Bipartite Binary Delta-matroids

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 813-821页

作者： Qi YAN Xian-an JIN School of Mathematics China University of Mining and TechnologyXuzhou 221116China School of Mathematical Sciences Xiamen UniversityXiamen 361005China

Delta-matroid theory is often thought of as a generalization of topological graph *** is well-known that an orientable embedded graph is bipartite if and only if its Petrie dual is *** this paper,we first introduce the concepts of Eulerian and bipartite delta-matroids and then extend the result from embedded graphs to arbitrary binary *** dual of any bipartite embedded graph is *** also extend the result from embedded graphs to the class of delta-matroids that arise as twists of binary *** related results are also obtained.

关键词： matroid delta-matroid binary bipartite Eulerian