Abstract
A linear $k$-forest is a graph whose components are paths with lengths at most $k$. The minimum number of linear $k$-forests needed to decompose a graph $G$ is the linear $k$-arboricity of $G$ and denoted by $la_{k}(G)$. In this paper, we settle the cases left in determining the linear $2$-arboricity of the complete graph $K_n$. Mainly, we prove that $la_{2} (K_{12t+10}) = la_{2}(K_{12t+11}) = 9t+8$ for any $t \geq 0$.
Citation
Chih-Hung Yen. Hung-Lin Fu. "LINEAR 2-ARBORICITY OF THE COMPLETE GRAPH." Taiwanese J. Math. 14 (1) 273 - 286, 2010. https://doi.org/10.11650/twjm/1500405741
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