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math.CO2025
Counterexamples to statements on isometric graph coverings
Paul Bastide, Julien Duron, Jędrzej Hodor +2
A connected subgraph of a graph is isometric if it preserves distances. In this short note, we provide counterexamples to several variants of the following general question: When a…
math.CO2025
Planar induced paths via a decomposition into non-crossing ordered graphs
Julien Duron, Hugo Jacob
In any graph, the maximum size of an induced path is bounded by the maximum size of a path. However, in the general case, one cannot find a converse bound, even up to an arbitrary…
math.CO2024
Adjacency Labeling Schemes for Small Classes
Édouard Bonnet, Julien Duron, John Sylvester +1
A graph class admits an implicit representation if, for every positive integer , its -vertex graphs have a -bit (adjacency) labeling scheme, i.e., their vertices c…