Given a digraph (an undirected graph, resp.) D and two positive integers f (x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)-factor if g(x) d + H (x) = d ? H (x) f (x)(g(x) d H (x) f (x), resp.) for every x 2 V (D). If f (x) = g(x) = 1 for every x, then a connected (g; f)-factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for ...

We prove that there is no degree of connectivity which will guarantee that a hypergraph contains two edge-disjoint spanning connected subhypergraphs. We also show that Edmonds’ theorem on arc-disjoint branchings cannot be extended to directed hypergraphs. Here we use a definition of a directed hypergraph that naturally generalizes the notion of a directed graph. For standard notation and result...

Inspired by a classic paper by Knuth, we revisit the problem of drawing flowcharts of loopfree algorithms, that is, degree-three series-parallel digraphs. Our drawing algorithms show that it is possible to produce Knuthian drawings of degree-three series-parallel digraphs with good aspect ratios and small numbers of edge bends.

I present an algorithm that, given a number $n \geq 1$, computes a compact representation of the set of all noncrossing acyclic digraphs with $n$ nodes. This compact representation can be used as the basis for a wide range of dynamic programming algorithms on these graphs. As an illustration, along with this note I am releasing the implementation of an algorithm for counting the number of noncr...

In this paper we investigate new sufficient conditions for a digraph to be kernel-perfect (KP) and some structural properties of kernel-perfect critical (KPC) digraphs. In particular, it is proved that the asymmetrical part of any KPC digraph is strongly connected. A new method to construct KPC digraphs is developed. The existence of KP and KPC digraphs with arbitrarily large dichromatic number...

Let G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial o...

Let G be an edge-bicolored graph where each edge is colored either red or blue. We study problems of obtaining an induced subgraph H from G that simultaneously satisfies given properties for H ’s red graph and blue graph. In particular, we considerDually Connected Induced Subgraph problem — find from G a k-vertex induced subgraph whose red and blue graphs are both connected, and Dual Separator ...

Theorem 1 was the starting point for many other suÆ ient onditions for = Æ. Lesniak [9℄ weakened the ondition Æ bn=2 to deg(u) + deg(v) n for all pairs of nonadja ent verti es u and v in G. Plesn k [10℄ showed that every graph of diameter 2 satis es = Æ and thus generalized Lesniak's result. Improvements of Plesn k's result an be found in Plesn k, Zn am [11℄ and Dankelmann, Volkmann [4℄ (see al...

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric...