Certifying Fully Dynamic Algorithms for Recognition and Hamiltonicity of Threshold and Chain Graphs

Abstract Solving problems on graphs dynamically calls for algorithms to function under repeated modifications the graph and be more efficient than solving problem whole from scratch after each modification. Dynamic have been considered several properties, example connectivity, shortest paths recognition. In this paper we present fully dynamic recognition of threshold chain graphs, which are optimal in sense that costs per modification linear number modified edges. Furthermore, our also consider addition deletion sets vertices as well negative case, i.e., where is not a or anymore, return certificate constant size. Additionally, Hamiltonian cycle path vertex cutset non-existence such case.