Meanwhile, comprehensive surveys on polynomial χ-binding functions have explored the parameterised connection between a graph’s clique number and its chromatic number, parsing out instances ...

One imperfect graph is a ring with an odd number of nodes, at least five, with each node connected just to its nearest neighbors. In this “odd hole,” only two nodes form a clique, but three ...

We consider a planning problem that generalizes Alcuin's river crossing problem to scenarios with arbitrary conflict graphs. This generalization leads to the so-called Alcuin number of the underlying ...

The dominant cliques of graph theory provide an unambiguous compartmentation for ecosystems. It is suggested here that it might make ecological sense to regard dominant cliques as something like ...

Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence ...