A matching in a graph is a set of edges, no two of which share an endpoint. We describe Edmond’s algorithm for finding matchings of maximum cardinality in a graph. For bipartite graphs with edge weights, we also show how to find matchings of maximum weight. It is recommended that the reader draws pictures of the various constructs that we use (such as alternating trees). I was too lazy to incor...

Consider the problem of maintaining a family F of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given S, S′ ∈ F , report every member of S ∩S′ in any order. We show that in the word RAM model, where w is the word size, given a cap d on the maximum size of any set, we can support set intersection queries in O( d w/ log2 w ) expected time, and updates in O...

Set constraints are inclusions between expressions denoting sets of trees. The eficiency of their satisfiabili ty test is a central issue in set-based program analysis, their main application domain. W e introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that i ts satisfiability problem as DEXPTIME-com...

In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...

Stick graphs are defined as follows. Let A (respectively B) be a set of vertical horizontal) segments in the plane such that bottom endpoints and left B lie on same ground line with slope −1. The graph by B, which is necessarily bipartite, intersection B. We answer an open problem showing recognizing NP-complete. This result allows us to easily solve two other problems, namely recognition BipHo...

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...

Bipartite graphs and permutation graphs are two well known subfamilies of the perfect graphs. Neither of these families is contained in the other, and their intersection is nonempty. This paper shows that graphs which are both bipartite and permutation graphs have good algorithmic properties. These graphs can be recognized in linear time, and several problems which are NP-complete or of unknown...