On Regular Factors in Regular Graphs with Small Radius
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 $k\le d$.
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1966 ◽
Vol 18
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pp. 1091-1094
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1986 ◽
Vol 41
(2)
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pp. 193-210
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1967 ◽
Vol 19
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pp. 644-648
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2000 ◽
Vol 9
(3)
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pp. 241-263
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