The question of when a given graph can be the underlying graph of a regular map has roots a hundred years old and is currently the object of several threads of research. This paper outlines this topic briefly and proves that a product of graphs which have regular embeddings also has such an embedding. We then present constructions for members of three families: (1) circulant graphs, (2) wreath ...

Following Jiang Guanghao and Xu Luoshan’s concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasiregular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually ...

We explore the regular-expression matching problem with respect to prefix-freeness of the pattern. We show that the prefix-free regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefix-free regular-expression matching problem. Furthermore, we suggest an algorithm to determine wheth...

For a matroid M , an element e such that both M \ e and M/e are regular is called a regular element of M . We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small size matroids, all 3-connected matroids in the class can be pieced together from F7 or S8 and a regular matroid using 3-sums. This result takes a step toward solving a probl...

However, the dodecahedron and the icosahedron can be realized with rational coordinates if we do not require them to be precisely regular: If you perturb the vertices of a regular icosahedron “just a bit” into rational position, then taking the convex hull will yield a rational polytope that is combinatorially equivalent to the regular icosahedron. Similarly, by perturbing the facet planes of a...

In this paper, we define hedge operation on a residuated skew lattice and investigate some its properties. We get relationships between some special sets as dense, nilpotent, idempotent, regular elements sets and their hedges.  By examples, we show that hedge of a dense element is not a dense and hedge of a regular element is not a regular. Also hedge of a nilpotent element is a nilpotent and h...

The Berge–Sauer conjecture (see [2, 3]) says that any simple (no multiple edges and loops) 4-regular graph contains a 3-regular subgraph. This conjecture was proved in [4, 6]. In [1, 2] the Chevalley–Warning theorem was used to extend this result to graphs with multiple edges, which are 4-regular plus an edge. Our main result, Theorem 2.2, presents the sufficient condition for a 4-regular graph...

The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.