English

Packing a number of copies of a $(p,\,q)$-graph

Combinatorics 2020-12-14 v2

Abstract

Let k,p,qk,p,q be three positive integers. A graph GG with order nn is said to be kk-placeable if there are kk edge disjoint copies of GG in the complete graph on nn vertices. A (p,q)(p,\,q)-graph is a graph of order pp with qq edges. Packing results have proved useful in the study of the complexity of graph properties. Bollob\'{a}s et al. investigated the kk-placeable of (n,n2)(n,\,n-2)-graphs and (n,n1)(n,\,n-1)-graphs with k=2k=2 and k=3k=3. Motivated by their results, this paper characterizes (n,n1)(n,\,n-1)-graphs with girth at least 99 which are 44-placeable. We also consider the kk-placeable of (n,n+1)(n,\,n+1)-graphs and 2-factors.

Keywords

Cite

@article{arxiv.2002.01266,
  title  = {Packing a number of copies of a $(p,\,q)$-graph},
  author = {Yun Wang and Jin Yan},
  journal= {arXiv preprint arXiv:2002.01266},
  year   = {2020}
}

Comments

16 pages,8 figures