منابع مشابه
Minors and Strong Products
Let G H and G2H denote, respectively, the strong and Cartesian products of graphs G and H . (We recall that K2 K2 is the complete graph K4 on four vertices, while K22K2 is a four-cycle C4.) Using a simple construction, we show that, for every bipartite G, the graph G K2 is a minor of the graph G2C4. In particular, the d-cube Qd has a complete minor on 2 (d+1)/2 vertices if d is odd, and on 3 · ...
متن کاملClique Minors in Cartesian Products of Graphs
A clique minor in a graph G can be thought of as a set of connected subgraphs in G that are pairwise disjoint and pairwise adjacent. The Hadwiger number η(G) is the maximum cardinality of a clique minor in G. It is one of the principle measures of the structural complexity of a graph. This paper studies clique minors in the Cartesian product G H. Our main result is a rough structural characteri...
متن کاملKazhdan-lusztig Immanants and Products of Matrix Minors
We define a family of polynomials of the form ∑ f(σ)x1,σ(1) · · ·xn,σ(n) in terms of the Kazhdan-Lusztig basis {C′ w(1) |w ∈ Sn} for the symmetric group algebra C[Sn]. Using this family, we obtain nonnegativity properties of polynomials of the form ∑ cI,I′∆I,I′(x)∆I,I′(x). In particular, we show that the application of certain of these polynomials to Jacobi-Trudi matrices yields symmetric funct...
متن کاملKazhdan-lusztig Immanants and Products of Matrix Minors, Ii
We show that for each permutation w containing no decreasing subsequence of length k, the Kazhdan-Lusztig immanant Immw(x) vanishes on all matrices having k equal rows or columns. Also, we define two filtrations of the vector space of immanants via products of matrix minors and pattern avoidance and use the above result to show that these filtrations are equivalent. Finally, we construct new an...
متن کاملInequalities in Products of Minors of Totally Nonnegative Matrices
Let I,I ′ be the minor of a matrix which corresponds to row set I and column set I ′. We give a characterization of the inequalities of the form I,I ′ K ,K ′ ≤ J,J ′ L ,L ′ which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2001
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0428