A. Kabela

activity

20152024

most citedNo additional tournaments are quasirandom-forcing

10 citations · 14 across the 14 of their papers we have counts for

collaborators

Showing math.COShow all

19 papers · 1 filter

math.CO2024

Every $3$ -connected ${K_{1, 3}, Γ_{3}}$ -free graph is Hamilton-connected

Adam Kabela, Zdeněk Ryjáček, Mária Skyvová +1

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

math.CO2024

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

Adam Kabela, Zdeněk Ryjáček, Mária Skyvová +1

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

math.CO2023

Packing $T$ -connectors in graphs needs more connectivity

Roman Čada, Adam Kabela, Tomáš Kaiser +1

Strengthening the classical concept of Steiner trees, West and Wu [J. Combin. Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$ -connector in a graph $G$ with a set…

math.CO2022

The number of abundant elements in union-closed families without small sets

Adam Kabela, Michal Polák, Jakub Teska

We let $F$ be a finite family of sets closed under taking unions and $\emptyset \neq \in F$ , and call an element abundant if it belongs to more than half of the…

math.CO2021

Density maximizers of layered permutations

Adam Kabela, Daniel Kral, Jonathan A. Noel +1

A permutation is layered if it contains neither 231 nor 312 as a pattern. It is known that, if $σ$ is a layered permutation, then the density of $σ$ in a permutation of order $n$ i…

math.CO2021

Forbidden induced pairs for perfectness and $ω$ -colourability of graphs

Maria Chudnovsky, Adam Kabela, Binlong Li +1

We characterise the pairs of graphs ${X, Y}$ such that all ${X, Y}$ -free graphs (distinct from $C_{5}$ ) are perfect. Similarly, we characterise pairs ${X, Y}$ such that a…

math.CO2021

Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4

Christoph Brause, Trung Duy Doan, Přemysl Holub +4

For every graph $X$ , we consider the class of all connected ${K_{1, 3}, X}$ -free graphs which are distinct from an odd cycle and have independence number at least $4$ , and we show…

math.CO2020

Hadwiger meets Cayley

Jacob W. Cooper, Adam Kabela, Daniel Král' +1

We show that every connected $k$ -chromatic graph contains at least $k^{k - 2}$ spanning trees.

math.CO2020

Coloring graphs by translates in the circle

Pablo Candela, Carlos Catala, Robert Hancock +4

The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base…

math.CO2020

Trestles in the squares of graphs

Adam Kabela, Jakub Teska

We show that the square of every connected $S (K_{1, 4})$ -free graph satisfying a matching condition has a $2$ -connected spanning subgraph of maximum degree at most~ $3$ . Furthermore,…

math.CO2019★ 10 cited

No additional tournaments are quasirandom-forcing

Robert Hancock, Adam Kabela, Daniel Kral +4

A tournament H is quasirandom-forcing if the following holds for every sequence (G_n) of tournaments of growing orders: if the density of H in G_n converges to the expected density…

math.CO2019

Packing and covering directed triangles asymptotically

Jacob W. Cooper, Andrzej Grzesik, Adam Kabela +1

A well-known conjecture of Tuza asserts that if a graph has at most $t$ pairwise edge-disjoint triangles, then it can be made triangle-free by removing at most $2 t$ edges. If true,…

math.CO2019

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

Adam Kabela, Zdeněk Ryjáček, Petr Vrána

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.CO2019

On forbidden induced subgraphs for K_{1,3}-free perfect graphs

Christoph Brause, Přemysl Holub, Adam Kabela +3

Considering connected $K_{1, 3}$ -free graphs with independence number at least $3$ , Chudnovsky and Seymour (2010) showed that every such graph, say $G$ , is $2 ω$ -colourable where $ω$ …

math.CO2017

Long paths and toughness of k-trees and chordal planar graphs

Adam Kabela

We show that every $k$ -tree of toughness greater than $\frac{k}{3}$ is Hamilton-connected for $k \geq 3$ . (In particular, chordal planar graphs of toughness greater than $1$ are Ha…

math.CO2017★ 1 cited

An update on non-Hamiltonian $\frac{5}{4}$ -tough maximal planar graphs

Adam Kabela

Studying the shortness of longest cycles in maximal planar graphs, we improve the upper bound on the shortness exponent of the class of $\frac{5}{4}$ -tough maximal planar graphs pr…

math.CO2016

Bounding the distance among longest paths in a connected graph

Jan Ekstein, Shinya Fujita, Adam Kabela +1

It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k>=7, Skupien in [7] obtained a connected graph in which some k longest paths have no c…

math.CO2015

10-tough chordal graphs are Hamiltonian

Adam Kabela, Tomáš Kaiser

Chen et al. proved that every 18-tough chordal graph has a Hamilton cycle [Networks 31 (1998), 29-38]. Improving upon their bound, we show that every 10-tough chordal graph is Hami…

math.CO2015★ 3 cited

Planar graphs have two-coloring number at most 8

Zdeněk Dvořák, Adam Kabela, Tomáš Kaiser

We prove that the two-colouring number of any planar graph is at most 8. This resolves a question of Kierstead et al. [SIAM J. Discrete Math.~23 (2009), 1548--1560]. The result is…

Every 3-connected {K1,3​,Γ3​}-free graph is Hamilton-connected

A closure for Hamilton-connectedness in {K1,3​,Γ3​}-free graphs

Packing T-connectors in graphs needs more connectivity

The number of abundant elements in union-closed families without small sets

Density maximizers of layered permutations

Forbidden induced pairs for perfectness and ω-colourability of graphs

Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4

Hadwiger meets Cayley

Coloring graphs by translates in the circle

Trestles in the squares of graphs

No additional tournaments are quasirandom-forcing

Packing and covering directed triangles asymptotically

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

On forbidden induced subgraphs for K_{1,3}-free perfect graphs

Long paths and toughness of k-trees and chordal planar graphs

An update on non-Hamiltonian 45​-tough maximal planar graphs

Bounding the distance among longest paths in a connected graph

10-tough chordal graphs are Hamiltonian

Planar graphs have two-coloring number at most 8

Every $3$ -connected ${K_{1, 3}, Γ_{3}}$ -free graph is Hamilton-connected

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

Packing $T$ -connectors in graphs needs more connectivity

Forbidden induced pairs for perfectness and $ω$ -colourability of graphs

An update on non-Hamiltonian $\frac{5}{4}$ -tough maximal planar graphs