A family $\mathcal{P}$ of subgraphs of $G$ is called a path cover (resp. a path partition) of $G$ if $\bigcup _{P\in \mathcal{P}}V(P)=V(G)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(G)$) and every element of $\mathcal{P}$ is a path. The minimum cardinality of a path cover (resp. a path partition) of $G$ is denoted by ${\rm pc}(G)$ (resp. ${\rm pp}(G)$). In this paper, we characterize the forbidden subgraph conditions assuring us that ${\rm pc}(G)$ (or ${\rm pp}(G)$) is bounded by a constant. Our main results introduce a new Ramsey-type problem.
@article{10_37236_10639,
author = {Shuya Chiba and Michitaka Furuya},
title = {Ramsey-type results for path covers and path partitions},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/10639},
zbl = {1503.05081},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10639/}
}
TY - JOUR
AU - Shuya Chiba
AU - Michitaka Furuya
TI - Ramsey-type results for path covers and path partitions
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10639/
DO - 10.37236/10639
ID - 10_37236_10639
ER -
%0 Journal Article
%A Shuya Chiba
%A Michitaka Furuya
%T Ramsey-type results for path covers and path partitions
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10639/
%R 10.37236/10639
%F 10_37236_10639
Shuya Chiba; Michitaka Furuya. Ramsey-type results for path covers and path partitions. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10639
