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Št. zadetkov: 3
Optimal bounds for zero-sum cycles. I. Odd order
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey, Raphael Steiner
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Oznake: Zero-sum Ramsey theory;directed cycles;Zero-sum cycles;
For a finite (not necessarily abelian) group Γ, let n(Γ) denote the smallest positive integer $n$ such that for each labelling of the arcs of the complete digraph of order n using elements from Γ, there exists a directed cycle such that the arc-labels along the cycle multiply to the identity. Alon a ...
Leto: 2025 Vir: Fakulteta za matematiko, naravoslovje in informacijske tehnologije Koper (UP FAMNIT)
A unified Erdős–Pósa theorem for cycles in graphs labelled by multiple abelian groups
Kevin Hendrey, O-joung Kwon, Sang-il Oum, Youngho Yoo, J. Pascal Gollin
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Oznake: Erdős-Pósa property;cycle packing;group-labelled graph;
In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs (l, z) of integers w ...
Leto: 2025 Vir: Fakulteta za matematiko, naravoslovje in informacijske tehnologije Koper (UP FAMNIT)
Clustered colouring of graph products
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey, Thomas Lesgourgues, Bojan Mohar, Youri Tamitegama, Jane Tan, David Richard Wood
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Oznake: graph products;colouring;clustering;
A colouring of a graph ▫$G$▫ has clustering ▫$k$▫ if the maximum number of vertices in a monochromatic component equals ▫$k$▫. Motivated by recent results showing that many natural graph classes are subgraphs of the strong product of a graph with bounded treewidth and a path, this paper studies clus ...
Leto: 2025 Vir: Fakulteta za matematiko in fiziko (UL FMF)
Št. zadetkov: 3
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