This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient algorithms problems that could not be solved by existing frameworks. To support this claim and illustrate the include output-polynomial several were known, including of bipartite subgraphs, -degenerate subgraphs (for bounded ), induced chordal trees. Usin...

In this paper we disprove a conjecture of Lidický and Murphy about the number copies given graph in $K_r$-free give an alternative general conjecture. We also prove asymptotically tight bound on any bipartite radius at most~$2$ triangle-free graph.

The subgraph isomorphism problem has various important applications, although it is generally NP-complete and difficult to solve. This paper examines the feasibility of a data dependent circuit for the subgraph isomorphism problem, which is particularly suitable for FPGA implementation. For graphs of 32 vertices, the average logic scale of data dependent circuits is only 5% of the corresponding...

In the (k, λ)-subgraph problem, we are given an undirected graph G = (V, E) with edge costs and two positive integers k and λ and the goal is to find a minimum cost simple λ-edge-connected subgraph of G with at least k nodes. This generalizes several classical problems, such as the minimum cost k-Spanning Tree problem or k-MST (which is a (k, 1)-subgraph), and minimum cost λ-edge-connected span...

We consider the MAXIMUM PLANAR SUBGRAPH problem given a graph G, nd a largest planar subgraph of G. This problem has applications in circuit layout, facility layout, and graph drawing. We improve to 4/9 the best known approximation ratio for the MAXIMUM PLANAR SUBGRAPH problem. We also consider a generalization of the previous problem, the MAXIMUM GENUS D SUBGRAPH problem-given a connected grap...