@article{18478,
  abstract     = {For a given graph G=(V,E), we define its \emph{nth subdivision} as the graph obtained from G by replacing every edge by a path of length n. We also define the \emph{mth power} of G as the graph on vertex set V where we connect every pair of vertices at distance at most m in G. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case m=n asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case m=n=3 in a strong sense.},
  author       = {Anastos, Michael and Boyadzhiyska, Simona and Rathke, Silas and Rué, Juanjo},
  issn         = {0166-218X},
  journal      = {Discrete Applied Mathematics},
  pages        = {506--511},
  publisher    = {Elsevier},
  title        = {{On the chromatic number of powers of subdivisions of graphs}},
  doi          = {10.1016/j.dam.2024.10.002},
  volume       = {360},
  year         = {2025},
}

@article{8793,
  abstract     = {We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff.},
  author       = {Zeiner, Martin and Schmid, Ulrich and Chatterjee, Krishnendu},
  issn         = {1872-6771},
  journal      = {Discrete Applied Mathematics},
  number       = {1},
  pages        = {392--415},
  publisher    = {Elsevier},
  title        = {{Optimal strategies for selecting coordinators}},
  doi          = {10.1016/j.dam.2020.10.022},
  volume       = {289},
  year         = {2021},
}

@article{5857,
  abstract     = {A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is [Formula presented](n−1), and that this bound is best possible for infinitely many values of n.},
  author       = {Fulek, Radoslav and Pach, János},
  issn         = {0166-218X},
  journal      = {Discrete Applied Mathematics},
  number       = {4},
  pages        = {266--231},
  publisher    = {Elsevier},
  title        = {{Thrackles: An improved upper bound}},
  doi          = {10.1016/j.dam.2018.12.025},
  volume       = {259},
  year         = {2019},
}

@article{5799,
  abstract     = {We construct a polyhedral surface called a graceful surface, which provides best possible approximation to a given sphere regarding certain criteria. In digital geometry terms, the graceful surface is uniquely characterized by its minimality while guaranteeing the connectivity of certain discrete (polyhedral) curves defined on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva (1999) and shown to be useful for triangular mesh discretization through graceful planes and graceful lines. In this paper we extend the considerations to a nonlinear object such as a sphere. In particular, we investigate the properties of a discrete geodesic path between two voxels and show that discrete 3D circles, circular arcs, and Mobius triangles are all constructible on a graceful sphere, with guaranteed minimum thickness and the desired connectivity in the discrete topological space.},
  author       = {Biswas, Ranita and Bhowmick, Partha and Brimkov, Valentin E.},
  issn         = {0166-218X},
  journal      = {Discrete Applied Mathematics},
  pages        = {362--375},
  publisher    = {Elsevier},
  title        = {{On the polyhedra of graceful spheres and circular geodesics}},
  doi          = {10.1016/j.dam.2015.11.017},
  volume       = {216},
  year         = {2017},
}

@article{4013,
  abstract     = {The shape of a protein is important for its functions, This includes the location and size of identifiable regions in its complement space. We formally define pockets as regions in the complement with limited accessibility from the outside. Pockets can be efficiently constructed by an algorithm based on alpha complexes. The algorithm is implemented and applied to proteins with known three-dimensional conformations. 1998 Published by Elsevier Science B.V. All rights reserved.},
  author       = {Edelsbrunner, Herbert and Facello, Michael and Liang, Jie},
  issn         = {0166-218X},
  journal      = {Discrete Applied Mathematics},
  number       = {1-3},
  pages        = {83 -- 102},
  publisher    = {Elsevier},
  title        = {{On the definition and the construction of pockets in macromolecules}},
  doi          = {10.1016/S0166-218X(98)00067-5},
  volume       = {88},
  year         = {1998},
}

@article{4025,
  abstract     = {Questions of chemical reactivity can often be cast as questions of molecular geometry. Common geometric models for proteins and other molecules are the space-filling diagram, the solvent accessible surface and the molecular surface. In this paper we present a new approach to triangulating the surface of a molecule under the three models, which is fast, robust, and results in topologically correct triangulations. Our computations are based on a simplicial complex dual to the molecule models. All proposed algorithms are parallelizable.},
  author       = {Akkiraju, Nataraj and Edelsbrunner, Herbert},
  issn         = {0166-218X},
  journal      = {Discrete Applied Mathematics},
  number       = {1-3},
  pages        = {5 -- 22},
  publisher    = {Elsevier},
  title        = {{Triangulating the surface of a molecule}},
  doi          = {10.1016/S0166-218X(96)00054-6},
  volume       = {71},
  year         = {1996},
}