A. Kabela

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math.CO2025

Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs

Adam Kabela, ZdenÄk RyjÃ¡Äek, Petr VrÃ¡na

We continue studying Thomassen's conjecture (every 4-connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2-…

math.CO2024

Every $3$ -connected ${K_{1, 3}, I^_{3}}$ -free graph is Hamilton-connected

Adam Kabela, ZdenÄk RyjÃ¡Äek, MÃ¡ria SkyvovÃ¡ +1

We show that every $3$ -connected ${K_{1, 3}, I^_{3}}$ -free graph is Hamilton-connected, where $I^_{3}$ is the graph obtained by joining two vertex-disjoint triangles with a path of len…

math.CO2024

A closure for Hamilton-connectedness in ${K_{1, 3}, I^_{3}}$ -free graphs

Adam Kabela, ZdenÄk RyjÃ¡Äek, MÃ¡ria SkyvovÃ¡ +1

We introduce a closure technique for Hamilton-connectedness of ${K_{1, 3}, I^_{3}}$ -free graphs, where $I^_{3}$ is the graph obtained by joining two vertex-disjoint triangles with a pa…

Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs

Every 3-connected {K1,3​,I^3​}-free graph is Hamilton-connected

A closure for Hamilton-connectedness in {K1,3​,I^3​}-free graphs

Every $3$ -connected ${K_{1, 3}, I^_{3}}$ -free graph is Hamilton-connected

A closure for Hamilton-connectedness in ${K_{1, 3}, I^_{3}}$ -free graphs