Multivariate matching polynomials of cyclically labelled graphs

The Complexity of Multivariate Matching Polynomials

We study various versions of the univariate and multivariate matching and rook polynomials. We show that there is most general multivariate matching polynomial, which is, up the some simple substitutions and multiplication with a prefactor, the original multivariate matching polynomial introduced by C. Heilmann and E. Lieb. We follow here a line of investigation which was very successfully purs...

Adaptive Matching Based Kernels for Labelled Graphs

Several kernels over labelled graphs have been proposed in the literature so far. Most of them are based on the Cross Product (CP) Kernel applied on decompositions of graphs into sub-graphs of specific types. This approach has two main limitations: (i) it is difficult to choose a-priori the appropriate type of sub-graphs for a given problem and (ii) all the sub-graphs of a decomposition partici...

Tutte Polynomials of Flower Graphs

Cyclically Orientable Graphs

Barot, Geiss and Zelevinsky define a notion of a “cyclically orientable graph” and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky’s work leaves open the question of giving an efficient characterization of cyclically orientable graphs. In this paper, we give a simple recursive description of cyclically orientable graphs, and use this to give ...

On cyclically embeddable graphs

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.