Add to ORKGWe study the exact complexity of the Hamiltonian Cycle and the q-Colouring problem in disk graphs. We show that the Hamiltonian Cycle problem can be solved in (formula presented) on n-vertex disk graphs where the ratio of the largest and smallest disk radius is O(1). We also show that this is optimal: assuming the Exponential Time Hypothesis, there is no (formula presented)-time algorithm for Hamiltonian Cycle, even on unit disk graphs. We give analogous results for graph colouring: under the Expo-nential Time Hypothesis, for any fixed q, q-Colouring does not admit a (formula presented)-time algorithm, even when restricted to unit disk graphs, and it is solvable in (formula presented)-time on disk graphs
Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \...
The q -Coloring problem asks whether the vertices of a graph can be properly colored with q colors. ...
Given a graph with colored edges, a Hamiltonian cycle is called alternating if its successive edges ...
We study the exact complexity of the Hamiltonian Cycle and the q-Colouring problem in disk graphs. W...
We study the exact complexity of the Hamiltonian Cycle and the q-Colouring problem in disk graphs. W...
In this paper, we prove that, given a clique-width k-expression of an n-vertex graph, Hamiltonian Cy...
International audienceIn this paper, we prove that, given a clique-width k-expression of an n-vertex...
We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst case t...
The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices o...
The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices o...
The Hamiltonian Cycle problem asks if an $n$-vertex graph $G$ has a cycle passing through all vertic...
The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle pas...
Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \...
The q -Coloring problem asks whether the vertices of a graph can be properly colored with q colors. ...
Given a graph with colored edges, a Hamiltonian cycle is called alternating if its successive edges ...
We study the exact complexity of the Hamiltonian Cycle and the q-Colouring problem in disk graphs. W...
We study the exact complexity of the Hamiltonian Cycle and the q-Colouring problem in disk graphs. W...
In this paper, we prove that, given a clique-width k-expression of an n-vertex graph, Hamiltonian Cy...
International audienceIn this paper, we prove that, given a clique-width k-expression of an n-vertex...
We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst case t...
The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices o...
The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices o...
The Hamiltonian Cycle problem asks if an $n$-vertex graph $G$ has a cycle passing through all vertic...
The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle pas...
Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \...
The q -Coloring problem asks whether the vertices of a graph can be properly colored with q colors. ...
Given a graph with colored edges, a Hamiltonian cycle is called alternating if its successive edges ...