Mrvar and Doreian recently defined a notion of bipartite clustering in bipartite signed graphs that gives a measure of imbalance of the signed graph, different from previous measures (the “frustration index” or “line index of balance”, l, and Davis’s clusterability). A biclustering of a bipartite signed graph is a pair (π1, π2) of partitions of the two color classes; the sets of the partitions ...

when the degree of saturation at intersection approaches one, webster’s optimum cycle length equation becomes inapplicable, because the cycle length will becomes very big when the degree of saturation approaches one and will be fully unrealistic when the degree of saturation becomes greater than one. this is not a problem for hcm2000 method. but optimum cycle length calculation in this method h...

υ(X,L) = lim sup k→∞ n! kn h(X,OX(kL)). If L is ample, or more generally nef and big, υ(L) = (L), the self-intersection number of L. The volume of a general big line bundle has been studied in [F] and [DEL]; in particular, υ(L) has been given the following geometric interpretation (Proposition 3.6 of [DEL]): Let (kL) [n] be the moving selfintersection number of kL, that is, the number of inters...

The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph Γ is distance-biregular when it is distance-regular around each vertex and the intersection array only depends on the stable set such a vertex belongs to. In this note we derive a new version of the sp...

The Dulmage–Mendelsohn decomposition (or the DM-decomposition) gives a unique partition of the vertex set of a bipartite graph reflecting the structure of all the maximum matchings therein. A bipartite graph is said to be DM-irreducible if its DM-decomposition consists of a single component. For connected bipartite graphs, this is equivalent to the condition that every edge is contained in some...

A bipartite graph G = (L,R;E) where V (G) = L∪R, |L| = p, |R| = q is called a (p, q)-tree if |E(G)| = p+ q − 1 and G has no cycles. A bipartite graph G = (L,R;E) is a subgraph of a bipartite graph H = (L′, R′;E′) if L ⊆ L′, R ⊆ R′ and E ⊆ E′. In this paper we present sufficient degree conditions for a bipartite graph to contain a (p, q)-tree.

For two xed graphs X and Y the X Y intersection graph of a graph G is a graph whose vertices are induced subgraphs of G isomor phic to Y and where two vertices are adjacent if their intersection in G contains an induced subgraph isomorphic to X A conformal k graph is a simple hypergraph whose hyperedges are exactly k cliques in the section of the hypergraph Let kX denote the disjoint union of k...

In 1986, Niwi nski 13] showed that the alternation hierarchy of the-calculus on binary trees without intersection was strict. But the xed-point terms he considered for proving this result are all equivalent to coB uchi terms (i.e. in 2) with intersection. Since then, the question of the strictness of the hierarchy of the-calculus on binary trees with intersection was open 4, 14]. Recently, and ...

We address the problem of computing bounds for the self-intersection number (the minimum number of self-intersection points) of members of a free homotopy class of curves in the doubly-punctured plane as a function of their combinatorial length L; this is the number of letters required for a minimal description of the class in terms of a set of standard generators of the fundamental group, and ...