Abstract We develop a theory of graph algebras over general fields. This is modelled after the developed by Freedman et al. (2007, J. Amer. Math. Soc. 20 37–51) for connection matrices, in study homomorphism functions real edge weight and positive vertex weight. introduce tensors properties. notion naturally generalizes concept matrices. It shown that counting perfect matchings, host other prop...

Let G be a directed graph. Its vertex-set will be denoted by X, and its arcs (or ‘directed edges’) are a subset of the Cartesian product X x X. A kernel of G is a subset S of X which is ‘stable’ (independent, i.e.: a vertex in S has no successor in S) and ‘absorbant’ (dominating, i.e. a vertex not in S has a successor in S). This concept has found many applications, for instance in cooperative ...

In this study, a spectral graph-theoretic grouping strategy for weakly supervised classification is introduced, where a limited number of labelled samples and a larger set of unlabelled samples are used to construct a larger annotated training set composed of strongly labelled and weakly labelled samples. The inherent relationship between the set of strongly labelled samples and the set of unla...

We investigate weakly-supervised image parsing, i.e., assigning class labels to image regions by using imagelevel labels only. Existing studies pay main attention to the formulation of the weakly-supervised learning problem, i.e., how to propagate class labels from images to regions given an affinity graph of regions. Notably, however, the affinity graph of regions, which is generally construct...

A perfect matching covering of a graph G is a set of perfect matchings of G such that every edge of G is contained in at least one member of it. Berge conjectured that every bridgeless cubic graph admits a perfect matching covering of order at most 5 (we call such a collection of perfect matchings a Berge covering of G). A cubic graph G is called a Kotzig graph if G has a 3-edge-coloring such t...

In nite perfect information extensive (FPIE) games, backward induction (BI) gives rise to all pure-strategy subgame perfect Nash equilibria, and iterative elimination of weakly dominated strategies (IEWDS) may give di erent outcomes for di erent orders of elimination. Duggan recently posed several conjectures in an e ort to better understand the relationship between BI and IEWDS in FPIE games. ...