A Note on Near-factor-critical Graphs

A near-factor of a finite simple graph $G$ is a matching that saturates all vertices except one. A graph $G$ is said to be near-factor-critical if the deletion of any vertex from $G$ results in a subgraph that has a near-factor. We prove that a connected graph $G$ is near-factor-critical if and only if it has a perfect matching. We also characterize disconnected near-factor-critical graphs.Comment: 4 page

THE STRATEGY OF MUSCULAR PRE-TENSION DURING INITIAL BLOCK PHASE IN SWIMMING GRAB START

The purpose of this study was to examine the effects of muscular pre-tension on swimming grab start performance. Eight well-trained subjects participated in this study. They were instructed to perform three strategies (stretch-shortening cycle, purely concentric with and with no muscular pre-tension) in grab start. Two Peak-Performance high-speed video cameras operating at 120 Hz and one Kistler force plate (600 Hz) mounted on the starting block were synchronized to collect the data. The results showed that the block time was significantly shorter and horizontal velocity of taking off was larger in muscular pre-tension than in stretch-shortening cycle strategy. Based on the results of the present study, it has been suggested that using muscular pre-tension strategy during initial block phase in grab start could add some benefits of decreasing time