Packing of graphic n-tuples

Packing of graphic n-tuples

An n-tuple π (not necessarily monotone) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} in which the degree of vi is the ith entry of π. Graphic n-tuples (d (1) 1 , . . . , d (1) n ) and (d (2) 1 , . . . , d (2) n ) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that dG1(vi) = d (1) i and dG2(vi) = d (2) i for all i. We prove that graphic n-tuples π1 and...

Packing of Graphic Sequences

Let π1 and π2 be graphic n-tuples, with π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) (they need not be monotone). We say that π1 and π2 pack if there exist edge-disjoint graphs G1 and G2 with vertex set {v1, . . . , vn} such that the degrees of vi in G1 and G2 are d (1) i and d (2) i , respectively. We prove that two graphic n-tuples pack if ∆ ≤ √ 2δn− (δ−1), where ∆ ...

Orbits on n-tuples

A transitive (infinite) permutation group which has m orbits on ordered pairs of distinct points has at least mn−1 orbits on ordered n-tuples. This is best possible, and groups attaining the bound can be characterised.

N-tuples and Cartesian Products for N = 5

This article deenes ordered n-tuples, projections and Cartesian products for n = 5. We prove many theorems concerning the basic properties of the n-tuples and Cartesian products that may be utilized in several further, more challenging applications. A few of these theorems are a strightforward consequence of the regularity axiom. The article originated as an upgrade of the article 3]. The artic...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups