Robert Jajcay

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4 papers · 1 filter

math.CO2025

On $(k, g)$ -Graphs without $(g + 1)$ -Cycles

Leonard Chidiebere Eze, Robert Jajcay, Jorik Jooken

A $(k, g, g + 1)$ -graph is a $k$ -regular graph of girth $g$ which does not contain cycles of length $g + 1$ . Such graphs are known to exist for all parameter pairs $k \geq 3,…

math.CO2025

Theoretical and Computational Approaches to Determining Sets of Orders for $(k, g)$ -Graphs

L. C. Eze, R. Jajcay, T. JajcayovÃ¡ +1

The Cage Problem requires for a given pair $k \geq 3, g \geq 3$ of integers the determination of the order of a smallest $k$ -regular graph of girth $g$ . We address a more general v…

math.CO2024

Analogues of Bermond-BollobÃ¡s Conjecture for Cages Yield Expander Families

Leonard Chidiebere Eze, Robert Jajcay

This paper presents a possible link between Cages and Expander Graphs by introducing three interconnected variants of the Bermond and BollobÃ¡s Conjecture, originally formulated in…

math.CO2024

On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration

Robert Jajcay, Jorik Jooken, IstvÃ¡n PorupsÃ¡nszki

A vertex-girth-regular $v g r (v, k, g, I^»)$ -graph is a $k$ -regular graph of girth $g$ and order $v$ in which every vertex belongs to exactly $I^»$ cycles of length $g$ . While all vertex-…

On (k,g)-Graphs without (g+1)-Cycles

Theoretical and Computational Approaches to Determining Sets of Orders for (k,g)-Graphs

Analogues of Bermond-BollobÃ¡s Conjecture for Cages Yield Expander Families

On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration

On $(k, g)$ -Graphs without $(g + 1)$ -Cycles

Theoretical and Computational Approaches to Determining Sets of Orders for $(k, g)$ -Graphs