Short cycle covers of graphs and nowhere-zero flows

2011 ◽  
Vol 68 (4) ◽  
pp. 340-348 ◽  
Author(s):  
Edita Máčajová ◽  
André Raspaud ◽  
Michael Tarsi ◽  
Xuding Zhu
Keyword(s):  
Short Cycle ◽  
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.

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

scholarly journals Short cycle covers and the cycle double cover conjecture

1992 ◽  
Vol 56 (2) ◽  
pp. 197-204 ◽  
Author(s):  
Ury Jamshy ◽  
Michael Tarsi
Keyword(s):  
Double Cover ◽  
Short Cycle ◽  
Cycle Covers

Short cycle covers of cubic graphs

1994 ◽  
Vol 18 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Genghua Fan
Keyword(s):  
Cubic Graphs ◽  
Short Cycle ◽  
Cycle Covers

scholarly journals Short Cycle Covers of Graphs with Minimum Degree Three

2010 ◽  
Vol 24 (1) ◽  
pp. 330-355 ◽  
Author(s):  
Tomáš Kaiser ◽  
Daniel Král' ◽  
Bernard Lidický ◽  
Pavel Nejedlý ◽  
Robert Šámal
Keyword(s):  
Minimum Degree ◽  
Short Cycle ◽  
Cycle Covers

Short Cycle Covers on Cubic Graphs by Choosing a 2-Factor

2016 ◽  
Vol 30 (4) ◽  
pp. 2086-2106 ◽  
Author(s):  
Barbora Candráková ◽  
Robert Lukoťka
Keyword(s):  
Cubic Graphs ◽  
Short Cycle ◽  
Cycle Covers

Technology of secondary purification by means of short-cycle unheated adsorption

1995 ◽  
Vol 31 (2) ◽  
pp. 123-124
Author(s):  
S. A. Sirotin ◽  
B. G. Berto
Keyword(s):  
Short Cycle

Short-cycle higher education and the pitfalls of collective action

Minerva ◽  
1976 ◽  
Vol 14 (1) ◽  
pp. 33-60 ◽  
Author(s):  
Raymond Boudon ◽  
Philippe Cibois ◽  
Janina Lagneau
Keyword(s):  
Higher Education ◽  
Collective Action ◽  
Short Cycle
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