The Chinese Postman Problem in a multigraph is the problem of finding a shortest closed walk traversing all the edges. In a (2r + 1)-regular multigraph, the problem is equivalent to finding a smallest spanning subgraph in which all vertices have odd degree. In 1994, Kostochka and Tulai established a sharp upper bound for the solution. In this paper, we give simple proofs of their bounds for 3-r...

The path packing problem is stated finding the maximum number of edge-disjoint paths between predefined pairs of nodes in an undirected multigraph. Such a multigraph together with predefined node pairs is often called a network. While in general the path packing problem is NP-hard, there exists a class of networks for which the hope of better solution for the path packing problem exists. In thi...

Aharoni and Berger conjectured that in any bipartite multigraph that is properly edge-coloured by n colours with at least n + 1 edges of each colour there must be a matching that uses each colour exactly once. In this paper we consider the same question without the bipartiteness assumption. We show that in any multigraph with edge multiplicities o(n) that is properly edge-coloured by n colours ...

n mathematical graph theory, coloring problems are ubiquitous. Dating back to the famous four-color map problem, both the theory and applications associated with graph coloring have a rich history. A standard problem in graph theory is to color a graph’s vertices with the fewest number of colors such that no two adjacent vertices have the same color. This article examines a complementary proble...

The architecture of a software system is typically defined as the organization of the system, the relationships among its components and the principles governing their design. By including artifacts coresponding to software engineering processes, the definition gets naturally extended into the architecture of a software system and process. In this paper we propose a holistic model to organize k...

In this paper lexical cohesion modeling is considered. We argue that to model lexical cohesion in connected texts it is not enough to find related words in a text. It is important to take into account relations between entities participating in the described situations. Consideration of this factor gives the possibility to develop more flexible lexical chaining algorithms and to construct lexic...

By Petersen’s theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least 3 has a spanning even subgraph in which every component has at least four vertic...

For a fixed multigraph H , possibly containing loops, with V (H) = {h1, . . . , hk}, we say a graph G is H -linked if for every choice of k vertices v1, . . . , vk in G, there exists a subdivision of H in G such that vi represents hi (for all i). This notion clearly generalizes the concept of k-linked graphs (as well as other properties). In this paper we determine, for a connected multigraph H...

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect ...