A k?coloring of an oriented graph G = (V; A) is an assignment c of one of the colors 1; 2; : : :; k to each vertex of the graph such that, for every arc (x; y) of G, c(x) 6 = c(y). The k?coloring is good if for every arc (x; y) of G there is no arc (z; t) 2 A such that c(x) = c(t) and c(y) = c(z). A k?coloring is said to be semi?strong if for every vertex x of G, c(z) 6 = c(t) for any pair fz; ...

In this paper we establish c-bit semi-external graph algorithms, – i.e., algorithms which need only a constant number c of bits per vertex in the internal memory. In this setting, we obtain new trade-offs between time and space for I/O efficient LTL model checking. First, we design a c-bit semi-external algorithm for depth-first search. To achieve a low internal memory consumption, we construct...

Let T = (V,E) be a tree. A core of T is a path P , such that the sum of the weighted distances from all vertices to this path is minimized. In this paper we consider the semi-obnoxious case where the vertices have positive or negative weights. We prove that if the sum of the weights of vertices is negative the core must be a single vertex and when the sum of the weights of vertices is zero ther...

The representations of dimension vector α of the quiver Q can be parametrised by a vector space R(Q,α) on which an algebraic group Gl(α) acts so that the set of orbits is bijective with the set of isomorphism classes of representations of the quiver. We describe the semi–invariant polynomial functions on this vector space in terms of the category of representations. More precisely, we associate...

We show that the dimension of the mesh algebra of a finite Auslander-Reiten quiver over a field is a purely combinatorial invariant that does not depend on the ground field. Moreover, a combinatorial algorithm for computing this dimension is given along our proof of this result. Translation quivers appear naturally in the representation theory of finite dimensional algebras; see, for example, [...

A key issue of semi-supervised clustering is how to utilize the limited but informative pairwise constraints. In this paper, we propose a new graph-based constrained clustering algorithm, named SCRAWL. It is composed of two random walks with different granularities. In the lower-level random walk, SCRAWL partitions the vertices (i.e., data points) into constrained and unconstrained ones, accord...

Let L be a Lie pseudoalgebra, a ∈ L. We show that, if a generates a (finite) solvable subalgebra S = 〈a〉 ⊂ L, then one may find a lifting ā ∈ S of [a] ∈ S/S such that 〈ā〉 is nilpotent. We then apply this result towards vertex algebras: we show that every finite vertex algebra V admits a decomposition into a semi-direct product V = U⋉N , where U is a subalgebra of V whose underlying Lie conforma...

William F. Klostermeyer Dept. Statistics and Computer Science West Virginia University Morgantown, WV 26506-6330 e-mail: [email protected] ABSTRACT A directed graph operation called pushing a vertex is studied. When a vertex is pushed, the orientation of each of its incident edges is reversed. We consider the problems of pushing vertices so as to produce strongly connected, semi-connected, and acy...

The aim is to predict the labeling of the vertices of a graph. The graph is given. A trial sequence of (vertex,label) pairs is then incrementally revealed to the learner. On each trial a vertex is given and the learner predicts a label and then the true label is returned. The learner’s goal is to minimize mistaken predictions. We propose to solve the problem by the method of best approximation....