Let G x H denote the Kronecker product of graphs G and H. Principal results are as follows: (a) If m is even and n 0 (mod 4), then one component of P,.+l x P,+1, and each component of each of CA x Pn+l, Pm+l x (7, and Cm x C, are edge decomposable into cycles of uniform length rs, where r and s are suitable divisors of m and n, respectively, (b) if m and n are both even, then each component of ...

Let F ={H1, . . . ,Hk} be a family of graphs. A graph G is called totally F -decomposable iffor every linear combination of the form α1e(H1) + · · · + αke(Hk) = e(G) where each αi is anonnegative integer, there is a coloring of the edges of G with α1 + · · · + αk colors such thatexactly αi color classes induce each a copy of Hi, for i = 1, . . . , k. We prove that if F i...

Su, X.-Y., A result on decompositions of regular graphs, Discrete Mathematics 105 (1992) 323-326. We prove that for any connected graph G and any integer r which is a common multiple of the degrees of the vertices in G, there exists a connected, r-regular, and G-decomposable graph H such that x(H) = x(G) and o(H) = w(G), where x and w are the chromatic number and the clique number, respectively...

Characterizations are given for the positive and completely positive maps on n n complex matrices that leave invariant the diagonal entries or the kth elementary symmetric function of the diagonal entries, 1 < k n. In addition, it was shown that such a positive map is always decomposable if n 3, and this fails to hold if n > 3. The real case is also considered.

‎recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎in this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎then we use this construction to generalize the result due to cook and nagel‎.

In maintaining consistencies, such as GAC*, FDGAC* and weak EDGAC*, for global cost functions, Weighted CSP (WCSP) solvers rely on the projection and extension operations, which entail the computation of the cost functions’ minima. Tractability of this minimum computation is essential for efficient execution. Since projections/extensions modify the cost functions, an important issue is tractabl...

Exact and asymptotic formulas for the mathematical expectation variance decomposable statistics generated by multidimensional Pólya random walks (with stopping border $$ G:{\sum}_{m=1}^N{k}_m=n ) are proposed, as well factorization double generating function of these statistics. Scenarios described when in scheme asymptotically normal (integral local limit theorems presented). Also, minimal (na...

A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is ∆5-categorical. We construct a computable completely decomposable group which is not ∆4-categorical, and give an example of a computable completely decomposable group G which is ∆4-categorical but not ∆3-categorical. We also prove that the inde...

A map ϕ : Mm(C) → Mn(C) is decomposable if it is of the form ϕ = ϕ 1 + ϕ 2 where ϕ 1 is a CP map while ϕ 2 is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map ϕ : M 2 (C) → M 2 (C) we construct concrete maps ϕ 1 and ϕ 2 which give a decomposition of ϕ. We also show that in most cases this decomposition is unique.

Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).