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3-biplacement of bipartite graphs

Adamus L., Leśniak E., Orchel B.

Opuscula Mathematica

2008

Vol. 28, no. 3

223-231

Let G = (L,R;E) be a bipartite graph with color classes L and R and edge set E. A set of two bijections {φ1, φ2}, φ1, φ2 : L ∪ R → L ∪ R, is said to be a 3-biplacement of G if [formula], where φ*/1, φ*/2 are the maps defined on E, induced by φ1, φ2, respectively. We prove that if ‌L‌ = p, ‌R‌ = q, 3 ≤ p ≤ q, then every graph G = (L, R; E) of size at most p has a 3-biplacement.

A note introducing Cayley graphs and group-coset graphs generated by graph packings

Rosiek R., Woźniak M.

Opuscula Mathematica

2004

Vol. 24, no. 2

203-221

The aim of this paper is to construct a class of vertex-transitive graphs that includes the Kneser graphs as a special case. The class will be based on the notion of packing of graphs. Certain families of graphs within this class will be examined more closely, and some of their properties, such as hamiltonicity, will be investigated.

Packing two copies of a tree into a planar graph

Woźniak M.

Opuscula Mathematica

2003

Vol. 23

95-97

A simple proof is given for a result of Garcia, Hernando, Hurtado, Noy and Tehel on packing of two copies of a tree into a planar graph.