Haruhide Matsuda

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Let a, b, k, and m be positive integers such that 1 ≤ a < b and 2 ≤ k ≤ (b + 1− m)/a. Let G = (V (G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b − 1) − 1)/b and |NG(x1) ∪ NG(x2) ∪ · · · ∪ NG(xk)| ≥ a|G|/(a+ b) for every independent set {x1, x2, . . . , xk} ⊆ V (G). Then for any subgraph H of G with m edges and δ(G−E(H)) ≥ a, G has an(More)
Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V (G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore’s theorem which guarantees the existence of a Hamilton path connecting any(More)
Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three. We show two sufficient conditions for a connected clawfree graph to have a spanning tree with a bounded number of branch vertices: (i) A connected claw-free graph has a spanning tree with at most k branch vertices if its independence number is at most 2k + 2.(More)
Let k ≥ 2 be an integer and G a 2-connected graph of order |G| ≥ 3 with minimum degree at least k. Suppose that |G| ≥ 8k − 16 for even |G| and |G| ≥ 6k − 13 for odd |G|. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ |G|/2 for each pair of nonadjacent vertices x and y in G. This is best possible in(More)