An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in polynomial time while the problems of finding a maximum Eulerian subgraph or a maximum induced Eulerian subgraph are NP-hard. In this paper, we ...

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism prob...

We investigate the computational complexity of the Densest k-Subgraph problem, where the input is an undirected graph G = (V,E) and one wants to find a subgraph on exactly k vertices with the maximum number of edges. We extend previous work on Densest k-Subgraph by studying its parameterized complexity for parameters describing the sparseness of the input graph and for parameters related to the...

Recently, Bacsó and Tuza gave a full characterization of the graphs for which every connected induced subgraph has a connected dominating subgraph satisfying an arbitrary prescribed hereditary property. Using their result, we derive a similar characterization of the graphs for which any isolate-free induced subgraph has a total dominating subgraph that satisfies a prescribed additive hereditary...

We consider the MINIMUM RAINBOW SUBGRAPH problem (MRS): Given a graph G whose edges are coloured with p colours. Find a subgraph F ⊆ G of minimum order and with p edges such that each colour occurs exactly once. This problem is NP-hard and APX-hard. For a given graph G and an edge colouring c with p colours we define the rainbow subgraph number rs(G, c) to be the order of a minimum rainbow subg...

ÐThis paper investigates the influence of the cost function on the optimal match between two graphs. It is shown that, for a given cost function, there are an infinite number of other cost functions that lead, for any given pair of graphs, to the same optimal error correcting matching. Furthermore, it is shown that well-known concepts from graph theory, such as graph isomorphism, subgraph isomo...