The adaption of combinatorial duality to infinite graphs has been hampered by the fact that while cuts (or cocycles) can be infinite, cycles are finite. We show that these obstruc...
We investigate the end spaces of infinite dual graphs. We show that there exists a natural homeomorphism between the end spaces of a graph and its dual, and that this homeomorphis...
Abstract. Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not in...
We use group theory to construct infinite families of maps on surfaces which are invariant under Wilson's map operations of order 3 but not under the operations of order 2, s...
By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a ...