SelectedWorks - Bernard Lidický

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Selected Works of Bernard Lidický

Associate Professor of Mathematics

Bernard Lidicky is currently an Associate Professor at Iowa State University. Lidicky received his PhD from Charles University in Prague (2007-2011). He then conducted post-doctoral research at University of Illinois, Urbana-Champaign (2011-2014).

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About Bernard Lidický

Bernard Lidicky is currently an Associate Professor at Iowa State University. Lidicky received his PhD from Charles University in Prague (2007-2011). He then conducted post-doctoral research at University of Illinois, Urbana-Champaign (2011-2014).

Peer-Reviewed Articles (47)

3‐Coloring Triangle‐Free Planar Graphs with a Precolored 8 ...

Journal of Graph Theory (2015)

zdeněk dvořák and Bernard Lidicky

Let G be a planar triangle-free graph and let C be a cycle in G of length at most 8. ...

Minimum Number of Monotone Subsequences of Length 4 in Permutations

Combinatorics, Probability and Computing (2015)

József Balogh, Ping Hu, Bernard Lidicky, Oleg Pikhurko, et al.

We show that for every sufficiently large n, the number of monotone subsequences of length four in a permutation on n points is ...

Planar 4-critical graphs with four triangles

European Journal of Combinatorics (2014)

Oleg V. Borodin, Zdeněk Dvořák, Alexandr V. Kostochka, Bernard Lidicky, et al.

By the Grünbaum–Aksenov Theorem (extending Grötzsch’s Theorem) every planar graph with at most three triangles is -colorable. However, there are ...

Short proofs of coloring theorems on planar graphs

European Journal of Combinatorics (2014)

Oleg V. Borodin, Alexandr V. Kostochka, Bernard Lidicky and Matthew Yancey

A lower bound on the number of edges in a -critical -vertex graph recently obtained by Kostochka and Yancey yields ...

4-Critical Graphs on Surfaces Without Contractible (≤4)-Cycles

SIAM Journal on Discrete Mathematics (2014)

Zdeněk Dvořák and Bernard Lidicky

We show that if G is a 4-critical graph embedded in a fixed surface Σ so that everycontractible cycle has ...

Upper bounds on the size of 4- and 6-cycle-free subgraphs ...

European Journal of Combinatorics (2014)

József Balogh, Ping Hu, Bernard Lidicky and Hong Liu

In this paper we modify slightly Razborov’s flag algebra machinery to be suitable for the hypercube. We use this modified ...

The Planar Slope Number of Planar Partial 3-Trees of Bounded ...

Graphs and Combinatorics (2013)

Vít Jelínek, Eva Jelínková, Jan Kratochvíl, Bernard Lidicky, et al.

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We ...

On the Turán Number of Forests

Electronic Journal of Combinatorics (2013)

Bernard Lidicky, Hong Liu and Cory Palmer

The Turan number of a graph H, ex(n;H), is the maximum number of edgesin a graph on n vertices which ...

Peeling the Grid

SIAM Journal on Discrete Mathematics (2013)

Sariel Har-Peled and Bernard Lidicky

Consider the set of points formed by the integer n × n grid and the process that ineach iteration removes ...

Finding vertex-surjective graph homomorphisms

Acta Informatica (2012)

Petr A Golovach, Bernard Lidicky, Barnaby Martin and Daniël Paulusma

The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism ...

Bipartizing fullerenes

European Journal of Combinatorics (2012)

Zdeněk Dvořák, Bernard Lidicky and Riste Škrekovskib

A fullerene graph is a cubic bridgeless planar graph with twelve 5-faces such that all other faces are 6-faces. We ...

Distance three labelings of trees

Discrete Applied Mathematics (2012)

Jiří Fiala, Petr A. Golovach, Jan Kratochvíl, Bernard Lidicky, et al.

An L (2,1,1)-labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that ...

Packing chromatic number of distance graphs

Discrete Applied Mathematics (2012)

Jan Ekstein, Přemysl Holub and Bernard Lidicky

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that vertices of G can ...

The k-in-a-Path Problem for Claw-free Graphs

Algorithmica (2012)

Jiří Fiala, Marcin Kamiński, Bernard Lidicky and Daniël Paulusma

The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is ...

Randić index and the diameter of a graph

European Journal of Combinatorics (2011)

Zdeněk Dvořák, Bernard Lidicky and Riste Škrekovski

The Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))−12 over ...

5-Coloring Graphs with 4 Crossings

SIAM Journal on Discrete Mathematics (2011)

Rok Erman, Bernard Lidicky, Frédéric Havet and Ondřej Pangrác

We answer in the negative a question of Oporowski and Zhao [Discrete Math., 309(2009), pp. 2948–2951] asking whether every graph ...

Graphs with Two Crossings Are 5-Choosable

SIAM Journal on Discrete Mathematics (2011)

Zdeněk Dvořák, Bernard Lidicky and Riste Škrekovski

A graph G is k-choosable if G can be properly colored whenever every vertex has alist of at least k ...

3-Choosability of Triangle-Free Planar Graphs with Constraints on 4-Cycles

SIAM Journal on Discrete Mathematics (2010)

Zdeněk Dvořák, Bernard Lidicky and Riste Škrekovski

A graph is k-choosable if it can be colored whenever every vertex has a list of at leastk available colors. ...

Short Cycle Covers of Graphs with Minimum Degree Three

SIAM Journal on Discrete Mathematics (2010)

Tomáš Kaiser, Bernard Lidicky, Daniel Král', Pavel Nejedlý, et al.

The shortest cycle cover conjecture of Alon and Tarsi asserts that the edges of everybridgeless graph with m edges can ...

The packing chromatic number of infinite product graphs

European Journal of Combinatorics (2009)

Jiří Fiala, Sandi Klavžar and Bernard Lidicky

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V(G) ...

3-choosability of plane graphs having no 3-, 6-, 7- and ...

Australasian Journal of Combinatorics (2009)

Bernard Lidicky

A graph is k-choosable if it can be colored whenever every vertex has alist of available colors of size at ...

6-critical graphs on the Klein bottle

SIAM Journal on Discrete Mathematics (2009)

Ken-Ichi Kawarabayashi, Daniel Král, Bernard Lidicky and Jan Kynčl

We provide a complete list of 6-critical graphs that can be embedded on the Kleinbottle settling a problem of Thomassen ...

Sharp bounds for decomposing graphs into edges and triangles

Acta Mathematica Universitatis Comenianae (2019)

Adam Blumenthal, Bernard Lidicky, Oleg Pikhurko, Yanitsa Pehova, et al.

Let pi3(G) be the minimum of twice the number of edges plus three times the number of triangles over all ...

Independent Sets near the Lower Bound in Bounded Degree Graphs

Leibniz International Proceedings in Informatics (2017)

Zdeněk Dvořák and Bernard Lidický

By Brook’s Theorem, every n-vertex graph of maximum degree at most ∆≥3 and clique number at most ∆ is ∆-colorable, ...

Markov decision processes for train run curve optimization

Electrical Systems for Aircraft, Railway and Ship Propulsion (ESARS), 2012 (2012)

Daniel Nikovski, Bernard Lidicky, Weihong Zhang, Kenji Kataoka, et al.

We propose three computationally efficient methods for finding optimal run curves of electrical trains, all based on the idea of ...