On polynomial time decidability of induced-minor-closed classes
On sampling colorings of bipartite graphs.
On some Interconnections Between Combinatorial Optimization and Extremal Graph Theory
On subgraphs without large components
We consider, for a positive integer , induced subgraphs in which each component has order at most . Such a subgraph is said to be -divided. We show that finding large induced subgraphs with this property is NP-complete. We also consider a related graph-coloring problem: how many colors are required in a vertex coloring in which each color class induces a -divided subgraph. We show that the problem of determining whether some given number of colors suffice is NP-complete, even for -coloring...
On the approximation of min split-coloring and min cocoloring.
On the complexity of covering nodes by K node-disjoint cycles
On the complexity of the subgraph problem
On the computational complexity of centers locating in a graph
It is shown that the problem of finding a minimum -basis, the -center problem, and the -median problem are -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal -center problem is also -complete.
On the computational complexity of (O,P)-partition problems
We prove that for any additive hereditary property P > O, it is NP-hard to decide if a given graph G allows a vertex partition V(G) = A∪B such that G[A] ∈ 𝓞 (i.e., A is independent) and G[B] ∈ P.
On the difficulty of finding walks of length k
On the distributed decision-making complexity of the minimum vertex cover problem
On the energy and spectral properties of the he matrix of hexagonal systems
The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles...
On the Horton-Strahler number for random tries
On the interchange heuristic for locating centers and medians in a graph
On the Number of Minimal 1-Steiner Trees.
On the parallel complexity of the alternating hamiltonian cycle problem
On the parallel complexity of the alternating Hamiltonian cycle problem
Given a graph with colored edges, a Hamiltonian cycle is called alternating if its successive edges differ in color. The problem of finding such a cycle, even for 2-edge-colored graphs, is trivially NP-complete, while it is known to be polynomial for 2-edge-colored complete graphs. In this paper we study the parallel complexity of finding such a cycle, if any, in 2-edge-colored complete graphs. We give a new characterization for such a graph admitting an alternating Hamiltonian cycle which allows...
On the proper intervalization of colored caterpillar trees
This paper studies the computational complexity of the proper interval colored graph problem (PICG), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the PICG and a graph layout problem the proper colored layout problem (PCLP). We show a dichotomy: the PICG and the PCLP are NP-complete for colored caterpillars of hair length ≥2, while both problems are in P for colored caterpillars of hair length <2. For...
On the size of minimal unsatisfiable formulas.
On the stack-size of general tries
Digital trees or tries are a general purpose flexible data structure that implements dictionaries built on words. The present paper is focussed on the average-case analysis of an important parameter of this tree-structure, i.e., the stack-size. The stack-size of a tree is the memory needed by a storage-optimal preorder traversal. The analysis is carried out under a general model in which words are produced by a source (in the information-theoretic sense) that emits symbols. Under some natural assumptions...