Anti-Ramsey theory in graphs is a branch of combinatorial mathematics that examines the conditions under which a graph, when its edges are coloured, must necessarily contain a ‘rainbow’ subgraph – a ...

Gallai–Ramsey theory lies at the intersection of graph colouring and Ramsey theory, providing a framework for understanding how structures emerge in edge-coloured graphs. Central to this domain is the ...

A spanning tree of a connected graph G is a subgraph of G that contains all the vertices in G and is a tree. A tree is an undirected graph that is connected and has no cycles. Breadth-First Search ...

Abstract: Determinating whether a graph is Hamiltonian is a open difficult problem. In this paper, the problem is converted to determinating whether the graph has a 2-regular Hamiltonian spanning ...