The bond and cycle spaces of an infinite graph
نویسندگان
چکیده
منابع مشابه
The bond and cycle spaces of an infinite graph
Bonnington and Richter defined the cycle space of an infinite graph to consist of the sets of edges of subgraphs having even degree at every vertex. Diestel and Kühn introduced a different cycle space of infinite graphs based on allowing infinite circuits. A more general point of view was taken by Vella and Richter, thereby unifying these cycle spaces. In particular, different compactifications...
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The edge space of a finite graph G = (V,E) over a field F is simply an assignment of field elements to the edges of the graph. The edge space can equally be thought of us an |E|-dimensional vector space over F. The cycle space and bond space are the subspaces of the edge space generated by the cycle and bonds of the graph respectively. It is easy to prove that the cycle space and bond space are...
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Casteels and Richter have shown that if X and Y are distinct compactifications of a locally finite graph G and f : X → Y is a continuous surjection such that f restricts to a homeomorphism on G, then the cycle space ZX of X is contained in the cycle space ZY of Y . In this work, we show how to extend a basis for ZX to a basis of ZY .
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Finite graph homology may seem trivial, but for infinite graphs things become interesting. We present a new approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of the unit circle in the space formed by the graph together with its ends. Our approach permits the extension to infinite graphs of standard results about fini...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2008
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20331