Edge-isoperimetric problems for Cartesian powers of regular graphs

Authors:
Sergei L. Bezrukov;Robert Elsässer
Affiliations:
Department of Mathematics and Computer Science, University of Wisconsin, Superior, Superior, WI;Department of Mathematics and Computer Science, University of Paderborn, Paderborn D-33102, Germany
Venue:
Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Year:
2003

Citing 1
Cited 3

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Abstract

We consider an edge-isoperimetric problem (EIP) on the Cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose Cartesian powers the lexicographic order provides nested solutions for the EIP. We present several new classes of such graphs that include as special cases all presently known graphs with this property. Our new results are applied to derive best possible edge-isoperimetric inequalities for the Cartesian powers of arbitrary regular, resp. regular bipartite, graphs with a high density.