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- Centre National de la Recherche ScientifiqueFR128 papers
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10 papers · 2 filters
On lower bounds for cardinalities of several separating-dominating codes in graphs
Dipayan Chakraborty, Annegret K. Wagler
In the literature, several different identification problems in graphs have been studied, the most widely studied such problems are the ones based on dominating sets as a tool of i…
Forest Cuts in Sparse Graphs
Vsevolod Chernyshev, Johannes Rauch, Dieter Rautenbach
We propose the conjecture that every graph of order with less than edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts a…
Identifying open codes in trees and 4-cycle-free graphs of given maximum degree
Dipayan Chakraborty, Florent Foucaud, Michael A. Henning
An identifying open code of a graph is a set of vertices that is both a separating open code (that is, for all distinct vertices and $…
The -bound for locating-dominating sets in subcubic graphs
Dipayan Chakraborty, Anni Hakanen, Tuomo Lehtilä
The location-domination number is conjectured to be at most half of the order for twin-free graphs with no isolated vertices. We prove that this conjecture holds and is tight for s…
Simple Chopsticks: Playing with any number of hands and fingers
Antoine Dailly, Valentin Gledel, Richard J. Nowakowski +1
Chopsticks is a game played by two players where they start with one finger raised on each hand. On their turn, each player moves by pointing an attacking hand at one of their oppo…
Complexity and algorithms for Arc-Kayles and Non-Disconnecting Arc-Kayles
Kyle Burke, Antoine Dailly, Nacim Oijid
Arc-Kayles is a game where two players alternate removing two adjacent vertices until no move is left, the winner being the player who played the last move. Introduced in 1978, its…