Related papers: Reducibility among NP-Hard graph problems and boun…

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…

We study Subgraph Isomorphism on graph classes defined by a fixed forbidden graph. Although there are several ways for forbidding a graph, we observe that it is reasonable to focus on the minor relation since other well-known relations lead…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

We initiate the study of spectral generalizations of the graph isomorphism problem. (a)The Spectral Graph Dominance (SGD) problem: On input of two graphs $G$ and $H$ does there exist a permutation $\pi$ such that $G\preceq \pi(H)$? (b) The…

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…

Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…

Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…

In a vertex-colored graph $G = (V, E)$, a subset $S \subseteq V$ is said to be consistent if every vertex has a nearest neighbor in $S$ with the same color. The problem of computing a minimum cardinality consistent subset of a graph is…

In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…

We strengthen a result by Laskar and Lyle (Discrete Appl. Math. (2009), 330-338) by proving that it is NP-complete to decide whether a bipartite planar graph can be partitioned into three independent dominating sets. In contrast, we show…

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree…

There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable structured class, such as the class of all planar graphs. Here we consider a general 'bridge-addable' class of graphs - if a graph…

Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…

Local Irregularity Conjecture states that every simple connected graph, except special cacti, can be decomposed into at most three locally irregular graphs, i.e., graphs in which adjacent vertices have different degrees. The connected…

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…

Let $G$ be a finite group and let $N$ be a normal subgroup of $G$. We attach to $N$ two graphs ${\Gamma}_G(N)$ and ${\Gamma}^{\ast}_G(N)$ related to the conjugacy classes of $G$ contained in $N$ and to the set of primes dividing the sizes…

We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

Graph modification problems are computational tasks where the goal is to change an input graph $G$ using operations from a fixed set, in order to make the resulting graph satisfy a target property, which usually entails membership to a…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…