@article{Chen2025, 
author = {Xiaohong Chen and Baoyindureng Wu},
title = {Gallai's path decomposition conjecture for block graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1438-1447},
keywords = {path decomposition, Gallai's conjecture, block graphs, cut vertex, end block},
url = {https://www.sciopen.com/article/10.3934/math.2025066},
doi = {10.3934/math.2025066},
abstract = {Let    G be a graph of order    n. A path decomposition        P   of    G is a collection of edge-disjoint paths that covers all the edges of    G. Let    p  (  G  ) denote the minimum number of paths needed in a path decomposition of    G. Gallai conjectured that if    G is connected, then    p  (  G  )  ≤  ⌈      n    2    ⌉. In this paper, we prove that the above conjecture holds for all block graphs.}
}