Therefore, if the cycle double cover conjecture is true, every biconnected graph has a circular embedding.
2.
All Hamiltonian graphs are biconnected, but a biconnected graph need not be Hamiltonian ( see, for example, the Petersen graph ).
3.
For instance, the SPQR tree of a biconnected graph is a representation of the graph as a 2-clique-sum of its triconnected components.
4.
Experimental work reported in for the Maximum flow problem, and in two papers by for the Graph Connectivity ( Connectivity ( graph theory ) ), Graph Biconnectivity ( biconnected graph ) and Graph Triconnectivity ( Triconnected component ) problems demonstrated that for some of the most advanced algorithms in the parallel algorithmic literature, the XMT paradigm can offer 8 times to over 100 times greater speedups than for the same problems on state-of-the-art multi-core computers.
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