Algebraic graph rewriting, which works by first removing the part of the graph to be regarded as garbage, and then gluing in the new part of the graph, is contrasted with term graph rewriting, which works by first gluing in the new part of the graph (the contractum) and performing redirections, and then removing garbage. It is shown that in the algebraic framework these two strategies can be re...

A graph G is called even if O(G)=<, and G is called eulerian if G is even and connected. If G has a spanning eulerian subgraph, then G is called supereulerian, and we write G # SL. Tutte [19, 20] and Matthews [17] conjectured that if a 2-edge-connected graph G has no subgraph contractible to the Petersen graph, then G has a 3-colorable double cycle cover (i.e., a collection of three even subgra...

A directed cycle double cover of a graph G is a family of cycles of G, each provided with an orientation, such that every edge of G is covered by exactly two oppositely directed cycles. Explicit obstructions to the existence of a directed cycle double cover in a graph are bridges. Jaeger [4] conjectured that bridges are actually the only obstructions. One of the difficulties in proving the Jaeg...

The union of two disjoint (n, 4n−1, 2) MDS codes in {0, 1, 2, 3}n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation in terms of n-quasigroups of order 4...

In a recent paper [9], the authors introduced the extended Q-bipartite double of an almost dual bipartite cometric association scheme. Since the association schemes arising from linked systems of symmetric designs are almost dual bipartite, this gives rise to a new infinite family of 4-class cometric schemes which are both Q-bipartite and Q-antipodal. These schemes, the schemes arising from lin...

In the framework of the double-pushout approach to graph grammars, we propose a new notion of parallel composition, called synchronized composition, of production applications. Our aim is to allow (pairs of) productions which are possibly not parallel independent, to be applied in parallel, provided that they are not mutually exclusive.The notion of synchronized composition we propose is not co...

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.