Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many efficient enumeration algorithms for the fundamental substructures such as spanning trees, cycles, and paths, have been developed. This paper addresses the enum...

We show new lower and upper bounds on the number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105n/10 ≈ 1.5926n such subgraphs, which improves an earlier lower bound by Schiermeyer (1996). We show an upper bound of n·12n/4 ≈ n·1.8613n and give an algorithm that lists all maximal induced bipartite subgraphs in time proportional ...

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdős and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.

An early characterization of distance-hereditary graphs is that every cycle of length 5 or more has crossing chords. A new, stronger, property is that in every cycle of length 5 or more, some chord has at least two crossing chords. This new property can be characterized by every block being complete multipartite, and also by the vertex sets of cycles of length 5 or more always inducing 3-connec...

We give the (Ahumada type) Selberg trace formula for a semiregular bipartite graph G: Furthermore, we discuss the distribution on arguments of poles of zeta functions of semiregular bipartite graphs. As an application, we present two analogs of the semicircle law for the distribution of eigenvalues of specified regular subgraphs of semiregular bipartite graphs. r 2003 Elsevier Science (USA). Al...

The partition of graphs into nice subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvabl...

This paper presents the application of metaheuristic methods to the minimum crossing number problem for the first time. These algorithms including particle swarm optimization, improved ray optimization, colliding bodies optimization and enhanced colliding bodies optimization. For each method, a pseudo code is provided. The crossing number problem is NP-hard and has important applications in eng...

This paper contains a new algorithm that recognizes whether a given graph G is a Hamming graph , i . e . a Cartesian product of complete graphs , in O ( m ) time and O ( n 2 ) space . Here m and n denote the numbers of edges and vertices of G , respectively . Previously this was only possible in O ( m log n ) time . Moreover , we present a survey of other recognition algorithms for Hamming grap...