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Path factors in cubic graphs
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On a k-Tree Containing Specified Leaves in a Graph
A k-tree of a graph is a spanning tree with maximum degree at most k. We give sufficient conditions for a graph G to have a k-tree with specified leaves: Let k,s, and n be integers such that k≥2,Expand
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Path factors in claw-free graphs
Abstract A graph G is called claw-free if G has no induced subgraph isomorphic to K1,3. We prove that if G is a claw-free graph with minimum degree at least d, then G has a path factor such that theExpand
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Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph
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 claw-free graph to have a spanning tree with aExpand
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The Global Relationship between Chromatin Physical Topology, Fractal Structure, and Gene Expression
Most of what we know about gene transcription comes from the view of cells as molecular machines: focusing on the role of molecular modifications to the proteins carrying out transcriptionalExpand
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On a Spanning Tree with Specified Leaves
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 hasExpand
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Ore-type conditions for the existence of even [2, b]-factors in graphs
  • H. Matsuda
  • Computer Science, Mathematics
  • Discret. Math.
  • 1 November 2005
For even b>=2, an even [2,b]-factor is a spanning subgraph each of whose degree is even between 2 and b. The main result is the following: a 2-edge-connected graph G of order n has an evenExpand
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On (g, f, n)-Critical Graphs
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Path factors in cubic graphs
Let ℱ be a set of connected graphs. An ℱ-factor of a graph is its spanning subgraph such that each component is isomorphic to one of the members in ℱ. Let Pk denote the path of order k. Akiyama andExpand
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Degree conditions for the existence of [k, k+1]-factors containing a given Hamiltonian cycle
  • H. Matsuda
  • Physics, Computer Science
  • Australas. J Comb.
  • 1 September 2002
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 +Expand
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