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Full-Text Articles in Computer Sciences
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. …