On the edge set of graphs of lattice paths
2004 ◽
Vol 2004
(61)
◽
pp. 3291-3299
This note explores a new family of graphs defined on the set of paths of them×nlattice. 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 thanksteps, wherekis a fixed parameter0=k=m+n. Each such graph is denoted byG(m,n,k). Two large complete subgraphs ofG(m,n,k)are described for all values ofm,n, andk. The size of the edge set is determined forn=2, and a complicated recursive formula is given for the size of the edge set whenk=1.
1994 ◽
Vol 52
◽
pp. 168-169
1989 ◽
Vol 47
◽
pp. 778-779
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2021 ◽
Vol 147
(3)
◽
pp. 04021001