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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Scholarship and Professional Work - LAS
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of edge-disjoint spanning trees of G. In this paper, we determine the minimum number of edges that must be added to G so that the resulting graph has spanning tree packing number at least k, for a given value of k.
Collapsible Graphs And Reductions Of Line Graphs, Zhi-Hong Chen, Peter C.B. Lam, Wai-Chee Shiu
Collapsible Graphs And Reductions Of Line Graphs, Zhi-Hong Chen, Peter C.B. Lam, Wai-Chee Shiu
Scholarship and Professional Work - LAS
A graph G is collapsible if for every even subset X ⊆ V ( G ) , G has a subgraph such that G − E ( Γ ) is connected and the set of odd-degree vertices of Γ is X . A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G . In this paper, we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between the line graph of the reduction and the reduction of the line graph. Our results extend former results in [H.-J. …
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Scholarship and Professional Work - LAS
We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.
The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen
The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen
Scholarship and Professional Work - LAS
The Hamiltonian index of a graph G is defined as h ( G ) = min { m : L m ( G ) is Hamiltonian } . In this paper, using the reduction method of Catlin [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44], we constructed a graph H ̃ ( m ) ( G ) from G and prove that if h ( G ) ≥ 2 , then h ( G ) = min{ m : H ̃ ( m ) ( G ) has a spanning Eulerian subgraph …