Year: 2023
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Hušek, Radek, Šámal, Robert
Institutions: Charles University, Czech Technical University in Prague
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4330339464