Properties of Large 2-Crossing-Critical Graphs

Domination and independence number of large $2$-crossing-critical graphs

“…Note that it would also be interesting to study other subclasses of graphs, especially graphs from (iv). However, like in [4], we restrict our studies to graphs from (i).…”

“…The above-mentioned large 3-connected 2-crossing-critical graphs have since attracted separate attention, see [4,7,22]. In [7,22], the Hamiltonicity of these graphs is discussed, and the number of all Hamiltonian cycles is determined.…”

“…In [7,22], the Hamiltonicity of these graphs is discussed, and the number of all Hamiltonian cycles is determined. In [4], several additional properties of large 3-connected 2-crossing-critical graphs have been studied. In particular, the number of vertices and edges can be determined from the signature of a graph, and several results regarding their chromatic number, chromatic index, and tree-width are presented.…”