On Regular Factors in Regular Graphs with Small Radius

Arne Hoffmann, Lutz Volkmann
2004 Electronic Journal of Combinatorics  
In this note we examine the connection between vertices of high eccentricity and the existence of $k$-factors in regular graphs. This leads to new results in the case that the radius of the graph is small ($\leq 3$), namely that a $d$-regular graph $G$ has all $k$-factors, for $k|V(G)|$ even and $k\le d$, if it has at most $2d+2$ vertices of eccentricity $>3$. In particular, each regular graph $G$ of diameter $\leq3$ has every $k$-factor, for $k|V(G)|$ even and $k\le d$.
doi:10.37236/1760 fatcat:wrywotgtxjbazgtxinvkxxolki