Counting circuit double covers
                        Autoři
                        
                                                                    
                            Hušek, R.; Šámal, R.
                        
                    
                        Rok
                        
                                                                    
                            2025
                        
                    
                        Publikováno
                        
                            
                            Journal of Graph Theory. 2025, 108(2), 374-395. ISSN 0364-9024.
                        
                    
                        Typ
                        
                                                                    
                                                    
                            Článek
                        
                    
                        Pracoviště
                        
                    
                                                                    
                        Anotace
                        
                            
                            We study a counting version of Cycle Double Cover Conjecture. We discuss why it is more interesting to count circuits (i.e., graphs isomorphic to C_k for some k) instead of cycles (graphs with all degrees even). We give an almost-exponential lower bound for graphs with a surface embedding of representativity at least 4. We also prove an exponential lower bound for planar graphs. We conjecture that any bridgeless cubic graph has at least 2^(n/2 - 1) circuit double covers and we show an infinite class of graphs for which this bound is tight.
                        
                    Group connectivity: Z4 vs Z22
                        Autoři
                        
                                                                    
                            Hušek, R.; Mohelníková, L.; Šámal, R.
                        
                    
                        Rok
                        
                                                                    
                            2020
                        
                    
                        Publikováno
                        
                            
                            Journal of Graph Theory. 2020, 93(3), ISSN 0364-9024.
                        
                    Homomorphisms of Cayley Graphs and Cycle Double Covers
                        Autoři
                        
                                                                    
                            Hušek, R.; Šámal, R.
                        
                    
                        Rok
                        
                                                                    
                            2020
                        
                    
                        Publikováno
                        
                            
                            Electronic Journal of Combinatorics (E-JC),. 2020, 27(2), ISSN 1077-8926.