Criterion for a Type of (g,f)-3-Covered Graphs

Abstract:

      First, $(g,f)$-3-covered graph is defined. A graph $G$ is called a $(g,f)$-3-covered graph if every three edges belong to a $(g,f)$-factor. Then a necessary and sufficient condition for a bipartite graph $G=(X,Y)$ to be $(g,f)$-3-covered is given when $g\leq f$. Moreover, a necessary and sufficient condition for a bipartitle graph $G=(X,Y)$ to be $f$-3-covered is obtained.