We investigate the Induced Subgraph Isomorphism problem with non-standard parametrization, where the parameter is the difference |V (G)| − |V (H)| with H and G being the smaller and the larger input graph, respectively. Intuitively, we can interpret this problem as “cleaning” the graph G, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph H represent...

Protein classification can be performed by representing 3-D protein structures by graphs and then classifying the corresponding graphs. One effective way to classify such graphs is to use frequent subgraph patterns as features; however, the effectiveness of using subgraph patterns in graph classification is often hampered by the large search space of subgraph patterns. In this paper, the author...

In this paper, we propose several integer programming (IP) formulations to exactly solve the minimum-cost λ -edge-connected k-subgraph problem, or the (k,λ )-subgraph problem, based on its graph properties. Special cases of this problem include the well-known k-minimum spanning tree problem (if λ = 1), λ -edgeconnected spanning subgraph problem (if k = |V |) and k-clique problem (if λ = k−1 and...

Let G be a graph and f : V (G) → {1, 3, 5, . . .}. Then a subgraph H of G is called a (1, f)-odd subgraph if degH(x) ∈ {1, 3, . . . , f(x)} for all x ∈ V (H). If f(x) = 1 for all x ∈ V (G), then a (1, f)-odd subgraph is nothing but a matching. A (1, f)-odd subgraph H of G is said to be maximum if G has no (1, f)-odd subgraph K such that |K| > |H|. We show that (1, f)-odd subgraphs have some pro...

In this paper we tackle the Sparsest k-Subgraph problem which consists in finding a subset of k vertices in a graph which induces the minimum number of edges. The Sparsest k-Subgraph problem is a natural generalization of the Independent Set problem, and thus is NP-hard (and even W [1]-hard) in general graphs. In this paper we investigate the parameterized complexity of both Sparsest k-Subgraph...

A graph G packs if for every induced subgraph H of G, the maximum number of vertexdisjoint cycles in H is equal to the minimum number of vertices whose deletion from H results in a forest. The purpose of this paper is to characterize all graphs that pack.

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex u is represented by a geometric object R(u) and each edge (u, v) is represented by the intersection between R(u) and R(v), if it belongs to a dense subgraph, or by a curve connecting the boundaries ofR(u) andR(v), otherwise. We study a notion of plana...

It is proved that every tree T on n > 2 vertices contains an induced subgraph F such that all its degrees are odd and 1 F 1 >rn/21,

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to ...