Author:
Aksenov V. A.,Borodin O. V.,Ivanova A. O.
Abstract
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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
10 articles.
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