A note on the path cover number of regular graphs
نویسندگان
چکیده
Let G be a simple graph of order n. The path cover number μ(G) is defined to be the minimum number of vertex disjoint paths required to cover the vertices of G. Ore proved that in general μ(G) ≤ max{1, n − σ2(G)}. We conjecture that if G is k-regular, then μ(G) ≤ n k+1 and we prove this for k ≤ 5.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 43 شماره
صفحات -
تاریخ انتشار 2009