Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three

Details Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three

2009-08-11

arxiv.org/abs/0908.1423v1

Mathematics

Combinatorics

Scientific paper

The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges of every bridgeless graph with $m$ edges can be covered by cycles of total length at most $7m/5=1.400m$. We show that every cubic bridgeless graph has a cycle cover of total length at most $34m/21\approx 1.619m$ and every bridgeless graph with minimum degree three has a cycle cover of total length at most $44m/27\approx 1.630m$.

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