แนวคิดหลัก
Hamiltonian path and Hamiltonian cycle problems are solvable in polynomial time for graphs with bounded independence number.
บทคัดย่อ
The content discusses the computational complexity of Hamiltonian path and Hamiltonian cycle problems in graphs, focusing on graphs with bounded independence number.
Key highlights:
Hamiltonian path and Hamiltonian cycle problems are NP-complete on general graphs, but the authors show that they can be solved in polynomial time for graphs with bounded independence number.
The authors introduce a more general problem called Hamiltonian-ℓ-Linkage, which asks if there exist ℓ disjoint paths that together cover all vertices of the graph. They prove that this problem is also solvable in polynomial time for graphs with bounded independence number.
As an application, the authors provide a complete characterization of the computational complexity of the L(2, 1)-labelling problem on H-free graphs and the related L′(2, 1)-labelling problem on triangle-free H-free graphs.
The authors present a recursive algorithm that solves the Hamiltonian-ℓ-Linkage problem by decomposing the graph into components based on a small vertex cut, and then solving the problem recursively on these components.