离散数学
We prove upper and lower bounds on the size of the largest square grid graph that is a subgraph, minor, or shallow minor of a graph in the form of a larger square grid from which a specified number of vertices have been deleted. Our bounds…
We derive a quadratic-time algorithm for the genus distribution of any 3-regular, biconnected series-parallel graph, which we extend to any biconnected series-parallel graph of maximum degree at most 3. Since the biconnected components of…
We show that if $G$ is a connected graph of maximum degree at most $4$, which is not $C_{2,5}$, then the strong matching number of $G$ is at least $\frac{1}{9}n(G)$. This bound is tight and the proof implies a polynomial time algorithm to…
Let $G$ be a simple graph with vertex set $V\left( G\right) $. A set $S\subseteq V\left( G\right) $ is independent if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the family of all independent sets of $G$. The…
The thesis consider the mixing of few (3-4) card shuffling as well as of large (52 card) deck. The thesis is showing the limit on the shuffling to homogeneity elaborated in short program; the thesis is in italian.
For a vertex $v$ of a graph $G$, a spanning tree $T$ of $G$ is distance-preserving from $v$ if, for any vertex $w$, the distance from $v$ to $w$ on $T$ is the same as the distance from $v$ to $w$ on $G$. If two vertices $u$ and $v$ are…
In this paper, we define irregular interval-valued fuzzy graphs and their various classifications. Size of regular interval-valued fuzzy graphs is derived. The relation between highly and neighbourly irregular interval-valued fuzzy graphs…
An L(2,1)-labelling of a graph $G=(V, E)$ is $\lambda_{2,1}(G)$ a function $f$ from the vertex set V (G) to the set of non-negative integers such that adjacent vertices get numbers at least two apart, and vertices at distance two get…
We study a new problem for cubic graphs: bipartization of a cubic graph $Q$ by deleting sufficiently large independent set $I$. It can be expressed as follows: \emph{Given a connected $n$-vertex tripartite cubic graph $Q=(V,E)$ with…
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree $\Delta$ has a strong edge-colouring with at most $4\Delta+4$ colours. We show…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
Let $G$ be a finite undirected graph. A vertex {\em dominates} itself and all its neighbors in $G$. A vertex set $D$ is an {\em efficient dominating set} (\emph{e.d.}\ for short) of $G$ if every vertex of $G$ is dominated by exactly one…
d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example,…
A word $w$ over an alphabet $\Sigma$ is a Lyndon word if there exists an order defined on $\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon…
We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then…
Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with…
This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local…
Equivalence relations on the edge set of a graph $G$ that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
According to the Erd\H{o}s discrepancy conjecture, for any infinite $\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy…