Weight of 3-Paths in Sparse Plane Graphs
Keyword(s):
We prove precise upper bounds for the minimum weight of a path on three vertices in several natural classes of plane graphs with minimum degree 2 and girth $g$ from 5 to 7. In particular, we disprove a conjecture by S. Jendrol' and M. Maceková concerning the case $g=5$ and prove the tightness of their upper bound for $g=5$ when no vertex is adjacent to more than one vertex of degree 2. For $g\ge8$, the upper bound recently found by Jendrol' and Maceková is tight.
2013 ◽
Vol 22
(6)
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pp. 935-954
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2018 ◽
Vol 27
(08)
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pp. 1850044
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1996 ◽
Vol 321
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pp. 335-370
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2012 ◽
Vol 10
(3)
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pp. 455-488
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2016 ◽
Vol 30
(4)
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pp. 622-639
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