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On the edge set of graphs of lattice paths

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  • Steven Klee
  • Lara Pudwell
  • Rick Gillman

Abstract

This note explores a new family of graphs defined on the set of paths of the m × n lattice. We let each of the paths of the lattice be represented by a vertex, and connect two vertices by an edge if the corresponding paths share more than k steps, where k is a fixed parameter 0 = k = m + n . Each such graph is denoted by G ( m , n , k ) . Two large complete subgraphs of G ( m , n , k ) are described for all values of m , n , and k . The size of the edge set is determined for n = 2 , and a complicated recursive formula is given for the size of the edge set when k = 1 .

Suggested Citation

  • Steven Klee & Lara Pudwell & Rick Gillman, 2004. "On the edge set of graphs of lattice paths," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:709624
    DOI: 10.1155/S0161171204306058
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