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Full-Text Articles in Computer Sciences
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
Zhi-Hong Chen
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 …
The Hamiltonian Index Of Graphs, Zhi-Hong Chen, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao
The Hamiltonian Index Of Graphs, Zhi-Hong Chen, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao
Zhi-Hong Chen
The Hamiltonian index of a graph GG is defined as h(G)=min{m:Lm(G) is Hamiltonian}.h(G)=min{m:Lm(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 sourceH̃^(m)(G) from GG and prove that if h(G)≥2h(G)≥2, then h(G) = min{m : H̃^(m)(G) has a spanning Eulerian subgraph}.
Spanning Eulerian Subgraphs In Claw-Free Graphs, Zhi-Hong Chen, Hong-Jian Lai, Weiqi Luo, Yehomg Shao
Spanning Eulerian Subgraphs In Claw-Free Graphs, Zhi-Hong Chen, Hong-Jian Lai, Weiqi Luo, Yehomg Shao
Zhi-Hong Chen
A graph is claw-free if it has no induced K 1,3, subgraph. A graph is essential 4-edge-connected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4-edge-connected claw free graph has a spanning Eulerian subgraph with maximum degree at most 4.
Spanning Trails Containing Given Edges, Weiqi Luo, Zhi-Hong Chen, Wei-Guo Chen
Spanning Trails Containing Given Edges, Weiqi Luo, Zhi-Hong Chen, Wei-Guo Chen
Zhi-Hong Chen
A graph G is Eulerian-connected if for any u and v in V ( G ) , G has a spanning ( u , v ) -trail. A graph G is edge-Eulerian-connected if for any e ′ and e ″ in E ( G ) , G has a spanning ( e ′ , e ″ ) -trail. For an integer r ⩾ 0 , a graph is called r -Eulerian-connected if for any X ⊆ E ( G ) with | X | ⩽ r , and for any u , v ∈ V ( G ) , G …
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
Zhi-Hong Chen
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. …