k - factors in regular graphs and edge - connectivity
نویسندگان
چکیده
Let , m , n , r be integers such that 2 ≤ ≤ r , r ≥ 4 and m , n ≥ 0 . Suppose G is an r -regular -edge-connected graph and that k is an even integer with m ≤ k ≤ r 2 . We say that G is an (m,n; k) -factor graph if for each disjoint pair E1, E2 ⊆ E(G) with |E1| = m and |E2| = n , G has a k -factor F such that E1 ⊆ E(F ) and E2 ∩E(F ) = ∅ . In this note we consider when G is an (m,n; k) -factor graph and characterize those graphs which fail for certain parameters ,m, n, r, k .
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