离散数学
In recent years, questions about the construction of special orderings of a given graph search were studied by several authors. On the one hand, the so called end-vertex problem introduced by Corneil et al. in 2010 asks for search orderings…
We prove that it is NP-hard to decide whether a graph is the square of a 6-apex graph. This shows that the square root problem is not tractable for squares of sparse graphs (or even graphs from proper minor-closed classes).
This paper extends the work started in 2002 by Demaine, Demaine and Verill (DDV) on coin-moving puzzles. These puzzles have a long history in the recreational literature, but were first systematically analyzed by DDV, who gave a full…
We define a $q$-linear path in a hypergraph $H$ as a sequence $(e_1,\ldots,e_L)$ of edges of $H$ such that $|e_i \cap e_{i+1}| \in [\![1,q]\!]$ and $e_i \cap e_j=\varnothing$ if $|i-j|>1$. In this paper, we study the connected components…
Given a set of squares and a strip of bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are…
For a fixed property (graph class) ${\Pi}$, given a graph G and an integer k, the ${\Pi}$-deletion problem consists in deciding if we can turn $G$ into a graph with the property ${\Pi}$ by deleting at most $k$ edges. The ${\Pi}$-deletion…
In this paper, we consider the lengths of cycles that can be embedded on the edges of the generalized pancake graphs which are the Cayley graph of the generalized symmetric group $S(m,n)$, generated by prefix reversals. The generalized…
The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its…
\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory.…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
Given a graph $G=(V,E)$, for a vertex set $S\subseteq V$, let $N(S)$ denote the set of vertices in $V$ that have a neighbor in $S$. Extending the concept of binding number of graphs by Woodall~(1973), for a vertex set $X \subseteq V$, we…
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry$\unicode{x2014}$the long-standing problem of determining if a projective plane of order ten exists. Both the original…
We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd $\beta$-cycle inequalities valid for this polytope, showed that these generally have…
The maximum edge colouring problem considers the maximum colour assignment to edges of a graph under the condition that every vertex has at most a fixed number of distinct coloured edges incident on it. If that fixed number is $q$ we call…
Rotor walks are cellular automata that determine deterministic traversals of particles in a directed multigraph using simple local rules, yet they can generate complex behaviors. Furthermore, these trajectories exhibit statistical…
In this paper, we investigate the graphs in which all balls are convex and the groups acting on them geometrically (which we call CB-graphs and CB-groups). These graphs have been introduced and characterized by Soltan and Chepoi (1983) and…
We introduce and study a new optimization problem on digraphs, termed Maximum Weighted Digraph Partition (MWDP) problem. We prove three complexity dichotomies for MWDP: on arbitrary digraphs, on oriented digraphs, and on symmetric digraphs.…
The break minimization problem is a fundamental problem in sports scheduling. Recently, its quadratic unconstrained binary optimization (QUBO) formulation has been proposed, which has gained much interest with the rapidly growing field of…
This paper considers two well-studied problems \textsc{Minimum Fill-In} (\textsc{Min Fill-In}) and \textsc{Treewidth}. Since both problems are \textsf{NP}-hard, various reduction rules simplifying an input graph have been intensively…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…