Báo cáo toán học: "Convexly independent subsets of the Minkowski sum of planar point sets" pdf

... and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P ⊕ Q which consist of convexly independent points. We show that, ... X of n points in the plane, what is the maximum number of pairs that can be selected from X so that the midpoints of their connecting segments are convexly indepe...

Ngày tải lên: 07/08/2014, 15:23

... more edges, then clearly G can be dominated by v together with a vertex of degree 2 taken from A. So we may assume that A has at most one edge. The sum of the degrees (in G) of the vertices of A ... v then v covers at least three vertices from A and then clearly γ(G) ≤ 4. Hence we may assume that |A v |≤2 for each v ∈ B. Note that the sum of the |A |’s is the num...

Ngày tải lên: 07/08/2014, 06:20

... (we follow the terminology of [4]). If G =(V,E)isak-critical graph, then the low-vertex subgraph of G, denoted by L(G), is the subgraph of G, induced by all vertices of degree k − 1. The high-vertex ... ingredient of our proof is the following result of Stiebitz. Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1. Then the number...

Ngày tải lên: 07/08/2014, 06:22

... set. the electronic journal of combinatorics 7 (2000), #R58 4 Hence g k = 0 and γ(n, δ) ≤ γ ∗ (n, δ) ≤ k. The theorem therefore follows from the definition of δ k+1 (n) which is the maximum value of ... k.Butγ(n, δ k (n)) ≥ k by definition of δ k (n). The theorem therefore follows. In the next section we show that if k = 3 then the above theorem holds for n ≥ 6. Note that...

Ngày tải lên: 07/08/2014, 06:22

... V , the character χ V belongs to the center of the group algebra C[S n ]. (5) The characters χ λ def = χ M λ are a vector-space basis for the center of the group algebra. (6) The center of the ... in one case and invalid in the other.) This lemma, together with the discussion preceding it, completes the proof of formula (18). We leave to the reader the task...

Ngày tải lên: 07/08/2014, 08:20

... Partition of the vertex set In the proof of the conjecture we will use two special sets, obtained by an operation of completion of a certain set to a set that dominates a specified set of vertices of ... subsets of the vertex set of a graph we say that A dominates (vertices of) B if every vertex of B has a neighbor in A or is a vertex of A.Wemaythen also say that...

Ngày tải lên: 07/08/2014, 08:22

... Proof of the main theorem By the recursive structure of rooted trees and the multiplicative properties of the cycle index, it is not difficult to see that Z = Z T (s 1 , s 2 , . . .) satisfies the ... exactly the number of different labelings of T , which finishes the proof.  3 Further applications Theorem 1 can also be applied to a general class of enumeration problems:...

Ngày tải lên: 07/08/2014, 13:21

... inv(σ) denote, resp ectively, the descent number and inversion number of σ in the symmetric group S n of degree n. We give an algebraic proof and a combinatorial proof of the recurrence relation. 1 ... q-recurrence relation is “semi” in the sense that the summands on the right involve two factors one of which depends on q whereas the other does not. We shall establish in...

Ngày tải lên: 08/08/2014, 11:20

... to the product of the weights of each of its entries, here the weight of entry s in T is taken to be the weight of the corner square containing s in the pa rt itio n obtained from the shape of ... is the the number of columns of height equal to the height of the column of i in the tableau obtained by removing all the entries j > i from T , and b...

Ngày tải lên: 08/08/2014, 12:22

... This completes the proof of (i). By a similar discussion as in the proof of (i), we may also show that (ii)-(iv) are true. We omit the procedure here. This completes the proof of Lemma 2.9. We ... − W the subgraph of G obtained by deleting the vertices of W a nd the edges incident with them. Similarly, if E ⊂ E(G), we denote by G − E the subgraph of G obtained by d...

Ngày tải lên: 08/08/2014, 12:22