Note: Partitioning powers of traceable or hamiltonian graphs

Authors:
Olivier Baudon;Julien Bensmail;Jakub Przybyło;Mariusz Woniak
Affiliations:
Univ. Bordeaux, LaBRI, UMR 5800, F-33400 Talence, France and CNRS, LaBRI, UMR 5800, F-33400 Talence, France;Univ. Bordeaux, LaBRI, UMR 5800, F-33400 Talence, France and CNRS, LaBRI, UMR 5800, F-33400 Talence, France;AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland;AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
Venue:
Theoretical Computer Science
Year:
2014

Citing 5
Cited 0

A linear algorithm for bipartition of biconnected graphs

Information Processing Letters
A linear-time algorithm for four-partitioning four-connected planar graphs

Information Processing Letters
Decomposable trees: a polynomial algorithm for tripodes

Discrete Applied Mathematics
Packing closed trails into dense graphs

Journal of Combinatorial Theory Series B
Decomposing trees with large diameter

Theoretical Computer Science

Quantified Score

Hi-index	5.23

Visualization

Abstract

A graph G=(V,E) is arbitrarily partitionable (AP) if for any sequence @t=(n"1,...,n"p) of positive integers adding up to the order of G, there is a sequence of mutually disjoint subsets of V whose sizes are given by @t and which induce connected graphs. If, additionally, for given k, it is possible to prescribe l=min{k,p} vertices belonging to the first l subsets of @t, G is said to be AP+k. The paper contains the proofs that the kth power of every traceable graph of order at least k is AP+(k-1) and that the kth power of every hamiltonian graph of order at least 2k is AP+(2k-1), and these results are tight.