Computing Cycle Covers without Short Cycles

2001 ◽  
pp. 368-379 ◽  
Author(s):  
Markus Bläser ◽  
Bodo Siebert
Keyword(s):  
Cycle Covers

scholarly journals Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Algorithmica ◽  
2005 ◽  
Vol 42 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Markus Bläser ◽  
Bodo Manthey
Keyword(s):  
Directed Graphs ◽  
Maximum Weight ◽  
Cycle Covers

scholarly journals Short Cycle Covers of Graphs with at Most 77% Vertices of Degree Two

10.37236/9284 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Anna Kompišová ◽  
Robert Lukot'ka
Keyword(s):  
Double Cover ◽  
Short Cycle ◽  
Cycle Cover ◽  
M 10 ◽  
Cycle Covers

Let $G$ be a bridgeless multigraph with $m$ edges and $n_2$ vertices of degree two and let $cc(G)$ be the length of its shortest cycle cover. It is known that if $cc(G) < 1.4m$ in bridgeless graphs with $n_2 \le m/10$, then the Cycle Double Cover Conjecture holds. Fan (2017)  proved that if $n_2 = 0$, then $cc(G) < 1.6258m$ and $cc(G) < 1.6148m$ provided that $G$ is loopless; morever, if $n_2 \le m/30$, then $cc(G) < 1.6467m$. We show that for a bridgeless multigraph with $m$ edges and $n_2$ vertices of degree two, $cc(G) < 1.6148m + 0.0741n_2$. Therefore, if $n_2=0$, then $cc(G) < 1.6148m$ even if $G$ has loops; if $n_2 \le m/30$, then $cc(G) < 1.6173m$; and if $n_2 \le m/10$, then $cc(G) < 1.6223|E(G)|$. Our improvement is obtained by randomizing Fan's construction.

scholarly journals 1-Factor and Cycle Covers of Cubic Graphs

2014 ◽  
Vol 78 (3) ◽  
pp. 195-206 ◽  
Author(s):  
Eckhard Steffen
Keyword(s):  
Cubic Graphs ◽  
Cycle Covers

Cubic Graphs with No Short Cycle Covers

2021 ◽  
Vol 35 (3) ◽  
pp. 2223-2233
Author(s):  
Edita Máčajová ◽  
Martin Škoviera
Keyword(s):  
Cubic Graphs ◽  
Short Cycle ◽  
Cycle Covers

Shortest cycle covers

2012 ◽  
pp. 163-188
Author(s):  
Cun-Quan Zhang
Keyword(s):  
Cycle Covers

scholarly journals Minimum-weight cycle covers and their approximability

2009 ◽  
Vol 157 (7) ◽  
pp. 1470-1480 ◽  
Author(s):  
Bodo Manthey
Keyword(s):  
Minimum Weight ◽  
Cycle Covers

Double cycle covers and the petersen graph

1989 ◽  
Vol 13 (4) ◽  
pp. 465-483 ◽  
Author(s):  
Paul A. Catlin
Keyword(s):  
Petersen Graph ◽  
Cycle Covers

scholarly journals Postman tours and cycle covers

1993 ◽  
Vol 111 (1-3) ◽  
pp. 447-454 ◽  
Author(s):  
André Raspaud
Keyword(s):  
Cycle Covers

scholarly journals Shortest cycle covers and cycle double covers with large 2-regular subgraphs

2013 ◽  
Vol 4 (4) ◽  
pp. 457-468
Author(s):  
Jonas Hägglund ◽  
Klas Markström
Keyword(s):  
Double Covers ◽  
Cycle Covers
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