Algorithms for classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of r-regular graphs of order 12 are here classified for r ≤ 6 and r = 10, 11. Two different approaches are used for regular graphs of small degree; these proceed one-factor by one-factor and vertex by vertex, respectively. For degree r = 11, we ...

We show that an n-vertex hypergraph with no r-regular subgraph has at most 2n−1 + r− 2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraph having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.

The main result of this paper is as follows: For any commutative regular (actually even K2-regular) ring R and any finitely generated intermediate monoid ZP+ c A4 c Q’+ (for some natural r) the following conditions are equivalent: (a) A4 zE:, (b) R[M] is K,-regular, (c) M is seminormal and SK,(R) = SK,(R[M]) (i.e. the natural homomorphism SK,(R) -SK,(R[M]) is an isomorphism), and, if in additio...

We construct highly edge-connected $r$-regular graph which do not contain $r-2$ pairwise disjoint perfect matchings. The results partially answer a question stated by Thomassen [Factorizing regular graphs, J. Comb. Theory Ser. B (2019), https://doi.org/10.1016/j.jctb.2019.05.002 (article in press)].

Let X,Y be finite sets, r,s,h,??N with s?r,X?Y. By ?Xh we mean the collection of all h-subsets X where each subset occurs ? times. A coloring (partition) is r-regular if element in exactly r subsets color. one-regular color class a perfect matching. We are interested necessary and sufficient conditions under which an can embedded into s-regular ?Yh. Using algebraic techniques involving glueing ...

In [4], Farran and Robertson extended the classical concept of regularity from convex polytopes to convex bodies in general. A convex body that is regular in this new sense is called a regular solid. Thus the set ^ of all regular polytopes is a subset of the set 5^ of all regular solids. Farran and Robertson constructed a projection P&R~> &R a d observed a close resemblance between this constru...

We show that if R is an exchange ring with primitive factors artinian then K1(R) U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1 | a,b ∈ R with 1+ab ∈ U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈ R. 2000 Mathematics Subject Classification. 16E50, 19B10. Very recently, Ara et al. [2] showed that the natural hom...

Let R be an integral domain, Star(R) the set of all star operations on and StarFC(R) finite type R. Then is said to regular if |Star(T)|≤|Star(R)| for every overring T In this paper we introduce notion finitely domain as such that |StarFC(T)|≤|StarFC(R)| each First, show notions domains are completely different do not imply other. Next, extend/generalize well-known results regularity in Noether...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...