Uniform Star-Factors of
Graphs with Girth Three
Yunjian
Wu 1 and Qinglin Yu 1, 2
1 Center for Combinatorics, LPMC, Nankai University, Tianjin
300071, P. R. China
2 Department of Mathematics and Statistics, Thompson Rivers
University, Kamloops, BC, Canada
Abstract Full Text PDF
A star-factor of a graph
$G$ is a spanning subgraph of $G$ such that each component of
which is a star. Recently, Hartnell and Rall studied a family
$\mathscr{U}$ of graphs $G$ satisfying the property that every
star-factor of $G$ has the same number of edges. They
characterized the structure of the family $\mathscr{U}$ with the
girth at least five. Our investigation focuses on graphs of
$\mathscr{U}$ with the girth three but without leaves and we are
able to determine this family of graphs.
