Geodesic
Weight of 3-paths in sparse plane graphs
The electronic journal of combinatorics, Tome 22 (2015) no. 3
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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.
DOI : 10.37236/4783
Classification : 05C22, 05C10, 05C42, 05C38
Mots-clés : planar graph, girth, 3-path, weight 
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     author = {V. A. Aksenov and O. V. Borodin and A. O. Ivanova},
     title = {Weight of 3-paths in sparse plane graphs},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {3},
     doi = {10.37236/4783},
     zbl = {1323.05058},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4783/}
}
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V. A. Aksenov; O. V. Borodin; A. O. Ivanova. Weight of 3-paths in sparse plane graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/4783

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