Computer Science Institute

Faculty of Mathematics and Physics, Charles University

Carl Feghali

I am a postdoctoral researcher at the Computer Science Institute of the Faculty of Mathematics and Physics of Charles University.

I obtained my Ph.D from Durham University in 2016 under the supervision of Matthew Johnson and Daniel Paulusma. Before coming to Charles, I was a postdoc at the University of Bergen and before that at Universite Paris Diderot.

My research interests include colorings and decompositions of graphs, combinatorial reconfiguration, combinatorial designs, extremal set theory and theoretical computer science.

Contact info : feghali.carl@gmail.com.

Teaching

Combinatorics and graph theory II (2020)

Co-authors

Faisal N. Abu-Khzam John Asplund Marthe Bonamy Peter Borg Nicolas Bousquet Pierre Charbit Christophe Crespelle Konrad Dabrowski Zdenek Dvorak Eduard Eiben Jiri Fiala Petr Golovach Pinar Heggernes Glenn Hurlbert Matthew Johnson Vikram Kamat Haiko Muller Giacomo Paesani Daniel Paulusma Pawel Rzazewski Robert Samal Daniel Thomas

Papers

(with O. Merkel) Mixing colourings in 2K2-free graphs, submitted.

Kempe equivalence of 4-critical planar graphs, submitted.

(with R. Samal) Decomposing a triangle-free planar graph into a forest and a subcubic forest, submitted.

(with P. Borg) The maximum sum of sizes of cross-intersecting families of subsets of a set, submitted.

(with P. Borg) A simple proof of Talbot's theorem for intersecting separated sets, submitted.

(with M. Bonamy, K. Dabrowski, M. Johnson and D. Paulusma) Recognizing graphs close to bipartite graphs with an application to colouring reconfiguration ,
Journal of Graph Theory, accepted.

(with Z. Dvorak) A Thomassen-type method for planar graph recoloring ,
European Journal of Combinatorics, 95 (2021) 103319.

Reconfiguring colorings of graphs with bounded maximum average degree,
Journal of Combinatorial Theory Series B 147 (2021) 133-138

(with Z. Dvorak) An update on reconfiguring 10-colorings of planar graphs,
The Electronic Journal of Combinatorics 27 (2020) P4.51.

(with P. Borg) The Hilton-Spencer cycle theorems via Katona's shadow intersection theorem,
Discussiones Mathematicae Graph Theory, in press.

(with G. Hurlbert, V. Kamat) An Erdos-Ko-Rado Theorem for unions of length 2 paths,
Discrete Mathematics, 12 (2020) 112121.

Reconfiguring 10-colourings of planar graphs,
Graphs and Combinatorics 36 (2020) 1815-1818.

(with K. Dabrowski, M. Johnson, G. Paesani, D. Paulusma, P. Rzazewski) On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest,
Algorithmica 82 (2020) 2841-2866.

(with E. Eiben), Towards Cereceda's conjecture for planar graphs.,
Journal of Graph Theory, 94 (2020), 267-277.

Intersecting families, signed sets, and injection
The Australasian Journal of Combinatorics, 76 (2020) 226-231.

(with J. Fiala) Reconfiguration graph for vertex colourings of weakly chordal graphs,
Discrete Mathematics, 343 (2020) 111733, 6 pp.

(with F. N. Abu-Khzam and P. Heggernes), Partitioning a graph into degenerate subgraphs,
European Journal of Combinatorics, 23 (2020) 103015.

(with J. Asplund and P. Charbit), Enclosings of decompositions of complete multigraphs in 2-edge-connected r-factorizations,
Discrete Mathematics 342 (2019) 2195-2203.

(with M. Bonamy, K. Dabrowski, M. Johnson and D. Paulusma) Independent feedback vertex set for P5-free graphs,
Algorithmica 81 (2019) 1342-1369.

Paths between colourings of graphs with bounded tree-width
Information Processing Letters 144 (2019) 37-38.

(with M. Bonamy, N. Bousquet and M. Johnson) On a conjecture of Mohar concerning Kempe equivalence of regular graphs,
Journal of Combinatorial Theory Series B 135 (2019) 179-199.

Paths between colourings of sparse graphs,
European Journal of Combinatorics 75 (2019), 169-171. doi

(with M. Johnson) Enclosings of decompositions of complete multigraphs in 2-factorizations,
Journal of Combinatorial Designs 26 (2018), 205-218. doi

(with M. Johnson and D. Thomas) Erdos-Ko-Rado theorems for a family of trees,
Discrete Applied Mathematics 236 (2018), 464-471. doi

(with M. Bonamy, K. Dabrowski, M. Johnson and D. Paulusma) Independent feedback vertex sets for graphs of bounded diameter,
Information Processing Letters 131 (2018), 26-32.doi

(with M. Johnson and D. Paulusma) A reconfigurations analogue of Brooks' theorem and its consequences,
Journal of Graph Theory 83 (2016), 340-358. doi

(with M. Johnson and D. Paulusma) Kempe equivalence of colourings of cubic graphs,
European Journal of Combinatorics 59 (2017), 1-10. doi

(with F. N. Abu-Khzam and H. Muller) Partitioning a graph into disjoint cliques and a triangle-free graph,
Discrete Applied Mathematics 190-191 (2015), 1-12. doi

Conference proceedings

(with C. Crespelle, P. A. Golovach) Cyclability in graph classes,
Proceedings of ISAAC 2019.

(with J. Fiala),
Reconfiguration graph for vertex colourings of weakly chordal graphs,
Proceedings of EuroComb 2019.

(with M. Johnson, G. Paesani, D. Paulusma),
On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest,
Proceedings of FCT 2019.

(with M. Bonamy, K. Dabrowski, M. Johnson and D. Paulusma),
Independent feedback vertex set for P5-free graphs,
Proceedings of ISAAC 2017, LIPIcs.
(with M. Bonamy, K. Dabrowski, M. Johnson and D. Paulusma),
Recognizing graphs close to bipartite graphs,
Proceedings of MFCS 2017, LIPIcs.
(with M. Johnson and D. Paulusma),
Kempe equivalence of colourings of cubic graphs,
Proceedings of EuroComb 2015, ENDM.
(with M. Johnson and D. Paulusma),
A reconfigurations analogue of Brooks' theorem,
Proceedings of MFCS 2014, LNCS.

Talks

Colorings and decompositions of planar graphs, Virginia Commonwealth University, March 2021.
Planar graph recoloring: two proofs, 55th Czech-Slovak Conference on Graph Theory 2020, Brno, Czech Republic, August 2020
Revisiting a theorem of Talbot, Midsummer Combinatorial workshop, Prague, Czech Republic, August 2020.
Graph theory meets extremal set theory, Charles University of Prague, Czech Republic, November 2019.
Kempe equivalence of regular graphs, University of Malta, June 2019.
Kempe equivalence of regular graphs, Bogazici University, April 2019.
Reconfiguring colourings of graphs with bounded maximum average degree, Combinatorial Reconfiguration Workshop, France 2019.
Paths between colourings of sparse graphs, Charles University of Prague, Czech Republic, January 2019.
Reconfiguration graphs, Durham University, UK December 2018
Paths between colourings of sparse graphs, Algorithms group, The University of Bergen, Norway, September 2018.
Erdos--Ko--Rado theorems for a family of trees, Alfred Renyi Institute of Mathematics, Hungary, April 2018.
Partitioning a graph into degenerate subgraphs, Algorithms group, The University of Bergen, Norway, January 2018.
Problems and Results in Kempe equivalence of colourings, Universite Paris Diderot, Paris, February 2017.
Problems and Results in Kempe equivalence of colourings, Society of Industrial and Applied Mathematics, USA, June 2016.
Kempe equivalence of colourings of cubic graphs, Durham University, UK, March 2016.
A reconfigurations analogue of Brooks' theorem, Durham University, UK, November 2015.
A reconfigurations analogue of Brooks' theorem, British Conference on Theoretical Computer Science, UK, March 2015.
A reconfigurations analogue of Brooks' theorem, Mathematical Foundations of Computer Science, Hungary, July 2014.
Partitioning a graph into disjoint cliques and a triangle-free graph, British Conference on Theoretical Computer Science, UK, March 2014.