An approximation algorithm for maximum P3-packing in subcubic graphs

We give a linear time 4/3-approximation algorithm for the problem of finding the maximum number of vertex-disjoint paths of order 3 in subcubic graphs without pendant vertices, which improves previously known results [K. Kawarabayashi, H. Matsuda, Y. Oda, K. Ota, Path factors in cubic graphs, Journal of Graph Theory 39 (2002) 188–193; A. Kelmans, D. Mubayi, How many disjoint 2-edge paths must a cubic graph have?, Journal of Graph Theory 45 (2004) 57–79].