66 citations · 323 across the 55 of their papers we have counts for
74 papers
There are no nontrivial chordal square-complementary graphs
Pierre Aboulker, Martin Milanič, Peter Muršič +1
We study square-complementary graphs (satisfying ). We show that in such graphs, no two vertices have comparable closed neighborhoods. This implies that…
On constrained intersection representations of graphs and digraphs
Ferdinando Cicalese, Clément Dallard, Martin Milanič
We study the problem of determining optimal directed intersection representations of DAGs in a model introduced by Kostochka, Liu, Machado, and Milenkovic [ISIT2019]: vertices are…
A tame vs. feral dichotomy for graph classes excluding an induced minor or induced topological minor
Martin Milanič, Nevena Pivač
A minimal separator in a graph is an inclusion-minimal set of vertices that separates some fixed pair of nonadjacent vertices. A graph class is said to be tame if there exists a po…
The Simultaneous Interval Number: A New Width Parameter that Measures the Similarity to Interval Graphs
Jesse Beisegel, Nina Chiarelli, Ekkehard Köhler +3
We propose a novel way of generalizing the class of interval graphs, via a graph width parameter called the simultaneous interval number. This parameter is related to the simultane…
On balanceable and simply balanceable regular graphs
Milad Ahanjideh, Martin Milanič, Mary Servatius
We continue the study of balanceable graphs, defined by Caro, Hansberg, and Montejano in 2021 as graphs such that any -coloring of the edges of a sufficiently large complete…
Tree decompositions meet induced matchings: beyond Max Weight Independent Set
Paloma T. Lima, Martin Milanič, Peter Muršič +3
For a tree decomposition of a graph , by we denote the size of a largest induced matching in all of whose edges intersect one bag of $\mathcal…
Treewidth versus clique number. IV. Tree-independence number of graphs excluding an induced star
Clément Dallard, Matjaž Krnc, O-joung Kwon +4
Many recent works address the question of characterizing induced obstructions to bounded treewidth. In 2022, Lozin and Razgon completely answered this question for graph classes de…
Allocation of Indivisible Items with a Common Preference Graph: Minimizing Total Dissatisfaction
Nina Chiarelli, Clément Dallard, Andreas Darmann +4
Allocating indivisible items among a set of agents is a frequently studied discrete optimization problem. In the setting considered in this work, the agents' preferences over the i…
Minimizing Maximum Dissatisfaction in the Allocation of Indivisible Items under a Common Preference Graph
Nina Chiarelli, Clément Dallard, Andreas Darmann +4
We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acycl…
Bisimplicial separators
Martin Milanič, Irena Penev, Nevena Pivač +1
A minimal separator of a graph is a set such that there exist vertices with the property that separates from in , b…
Fair Allocation Algorithms for Indivisible Items under Structured Conflict Constraints
Nina Chiarelli, Matjaž Krnc, Martin Milanič +2
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds t…
Functionality of box intersection graphs
Clément Dallard, Vadim Lozin, Martin Milanič +2
Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that…
Computing Well-Covered Vector Spaces of Graphs using Modular Decomposition
Martin Milanič, Nevena Pivač
A graph is well-covered if all its maximal independent sets have the same cardinality. This well studied concept was introduced by Plummer in 1970 and naturally generalizes to the…
Tree decompositions with bounded independence number: beyond independent sets
Martin Milanič, Paweł Rzążewski
We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-in…
Avoidability beyond paths
Vladimir Gurvich, Matjaž Krnc, Martin Milanič +1
The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simpli…
Treewidth versus clique number. III. Tree-independence number of graphs with a forbidden structure
Clément Dallard, Martin Milanič, Kenny Štorgel
We continue the study of -bounded graph classes, that is, hereditary graph classes in which the treewidth can only be large due to the presence of a large clique,…
Allocation of Indivisible Items with Individual Preference Graphs
Nina Chiarelli, Clément Dallard, Andreas Darmann +5
This paper studies the allocation of indivisible items to agents, when each agent's preferences are expressed by means of a directed acyclic graph. The vertices of each preference…
Treewidth versus clique number. II. Tree-independence number
Clément Dallard, Martin Milanič, Kenny Štorgel
In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call -bounded. W…
Graphs with at most two moplexes
Clément Dallard, Robert Ganian, Meike Hatzel +2
A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. While every non-complete graph has at least two mopl…
Complexity and algorithms for constant diameter augmentation problems
Eun Jung Kim, Martin Milanic, Jérôme Monnot +1
We study the following problem: for given integers and graph , can we obtain a graph with diameter via at most edge deletions ? We determine the computational comp…
On the degree sequences of dual graphs on surfaces
Endre Boros, Vladimir Gurvich, Martin Milanič +1
Given two graphs and with a one-to-one correspondence between their edges, when do and form a pair of dual graphs realizing the vertices and countries of a map…
Shifting paths to avoidable ones
Vladimir Gurvich, Matjaž Krnc, Martin Milanič +1
An extension of an induced path in a graph is an induced path such that deleting the endpoints of results in . An induced path in a graph is said to be avoidab…
Strong cliques in diamond-free graphs
Nina Chiarelli, Berenice Martínez Barona, Martin Milanič +2
A strong clique in a graph is a clique intersecting all inclusion-maximal stable sets. Strong cliques play an important role in the study of perfect graphs. We study strong cliques…
Treewidth versus clique number. I. Graph classes with a forbidden structure
Clément Dallard, Martin Milanič, Kenny Štorgel
Treewidth is an important graph invariant, relevant for both structural and algorithmic reasons. A necessary condition for a graph class to have bounded treewidth is the absence of…