Short Cycle Covers of Graphs with Minimum Degree Three
نویسندگان
چکیده
The Shortest Cycle Cover Conjecture asserts that the edges of every bridgeless graph with m edges can be covered by cycles of total length at most 7m/5 = 1.4m. We show that every bridgeless graph with minimum degree three that contains m edges has a cycle cover comprised of three cycles of total length at most 44m/27 ≈ 1.6296m; this extends a bound of Fan [J. Graph Theory 18 (1994), 131–141] for cubic graphs to the class of all graphs with minimum degree three.
منابع مشابه
Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three
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 ≈ 1.619m and every bridgeless graph with minimum degree three has a cycle cover of total length at most 44m/27 ≈ 1.630m.
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 24 شماره
صفحات -
تاریخ انتشار 2010