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math.CO2026
An Erdős-Pósa theorem for induced packings of even cycles
Jungho Ahn, Lars Jaffke, O-joung Kwon +2
We show that for every graph and every positive integer , contains either vertex-disjoint even cycles with no edges between distinct cycles, or a set of $O(k^2\log k…
math.CO2026
Erdős-Pósa property for induced packings of long -cycles
Jungho Ahn, O-joung Kwon
The Erdős-Pósa theorem states that for every integer , every graph contains either vertex-disjoint cycles or a set of vertices meeting all cycles…
math.CO2026
Optimal b-Colourings and Fall Colourings in -Free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke +3
In a colouring of a graph, a vertex is b-chromatic if it is adjacent to a vertex of every other colour. We consider four well-studied colouring problems: b-Chromatic Number, Tight…