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The path space of a higher-rank graph

Samuel B. G. Webster (2011)

Studia Mathematica

We construct a locally compact Hausdorff topology on the path space of a finitely aligned k-graph Λ. We identify the boundary-path space ∂Λ as the spectrum of a commutative C*-subalgebra D Λ of C*(Λ). Then, using a construction similar to that of Farthing, we construct a finitely aligned k-graph Λ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ∂Λ̃. We show that when Λ is row-finite, we can identify C*(Λ) with a full corner of C*(Λ̃), and deduce that D Λ is isomorphic...

The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.

Total edge-domatic number of a graph

Bohdan Zelinka (1991)

Mathematica Bohemica

The total edge-domatic number of a graph is introduced as an edge analogue of the total domatic number. Its values are studied for some special classes of graphs. The concept of totally edge-domatically full graph is introduced and investigated.

Two operations of merging and splitting components in a chain graph

Milan Studený, Alberto Roverato, Šárka Štěpánová (2009)

Kybernetika

In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use...

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