搜索结果: 196-210 共查到“组合数学”相关记录584条 . 查询时间(2.576 秒)
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth p...
南开大学陈永川当选中国科学院院士（图）
南开大学 陈永川 中国科学院 院士
2012/2/3
2011年12月9日，中国科学院公布2011年院士增选结果，南开大学教授、组合数学研究中心主任陈永川当选中国科学院数学物理学部院士。截至目前，南开共有两院院士12名。
Abstract: The existence question for tiling of the $n$-dimensional Euclidian space by crosses is well known. A few existence and nonexistence results are known in the literature. Of special interest a...
Abstract: Let M be a subset of {0, .., n} and F be a family of subsets of an n element set such that the size of A intersection B is in M for every A, B in F. Suppose that l is the maximum number of c...
The 1/3-2/3 conjecture for $N$-free ordered sets
Ordered set Linear extension N-free Balanced pair 1/3-2/3 Conjecture
2011/9/22
Abstract: A balanced pair in a finite ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of linear extensions of $P$ that put $x$ before $y$ is in the real interval...
The solution space geometry of random linear equations
solution space geometry random linear equations Data Structures and Algorithms
2011/10/9
Abstract: We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In partic...
Edge-coloring series-parallel multigraphs
Edge-coloring series-parallel multigraphs Data Structures and Algorithms Combinatorics
2011/10/9
Abstract: We give a simpler proof of Seymour's Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colore...
Maximum spectral radius of graphs with given connectivity and minimum degree
connectivity spectral radius Combinatorics
2011/9/21
Abstract: Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most $k$, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order $n$ with $\kappa(G) \...
The size of a hypergraph and its matching number
hypergraph its matching number Combinatorics
2011/9/22
Abstract: More than forty years ago, Erd\H{o}s conjectured that for any T <= N/K, every K-uniform hypergraph on N vertices without T disjoint edges has at most max{\binom{KT-1}{K}, \binom{N}{K} - \bin...
The adjacency matroid of a graph
adjacency delta-matroid interlace polynomial local complement matroid minor Tutte polynomial
2011/9/22
Abstract: If $G$ is a looped graph, then its adjacency matrix represents a binary matroid $M_{A}(G)$ on $V(G)$. $M_{A}(G)$ may be obtained from the delta-matroid represented by the adjacency matrix of...
Invariant number triangles, eigentriangles and Somos-4 sequences
Invariant number triangles eigentriangles Somos-4 sequences Combinatorics
2011/9/22
Abstract: Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invarian...
Abstract: Extending Furstenberg's ergodic theoretic proof for Szemer\'edi's theorem on arithmetic progressions, Furstenberg and Weiss (2003) proved the following qualitative result. For every d and k,...
Monochromatic cycles and the monochromatic circumference in 2-coloured graphs
Monochromatic cycles monochromatic circumference 2-coloured graphs
2011/9/21
Abstract: Li, Nikiforov and Schelp conjectured that a 2-edge coloured graph G with order n and minimal degree strictly greater than 3n/4 contains a monochromatic cycle of length l, for all l at least ...
Abstract: Let $S$ be a set of $n$ points in the unit square $[0,1]^2$, one of which is the origin. We construct $n$ pairwise interior-disjoint axis-aligned empty rectangles such that the lower left co...
The Mobius function of generalized subword order
Chebyshev polynomial discrete Morse theory homotopy type minimal skipped interval Mobius function
2011/9/20
Abstract: Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \le w if and only if there is a subword u...