TY - JOUR
T1 - Describing 3-paths in normal plane maps
AU - Borodin, O. V.
AU - Ivanova, A. O.
AU - Jensen, T. R.
AU - Kostochka, A. V.
AU - Yancey, M. P.
N1 - Funding Information:
The first author’s work was supported by grants 12-01-00631 and 12-01-00448 of the Russian Foundation for Basic Research . The second author was supported by grant 12-01-98510 of the Russian Foundation for Basic Research . The third author’s research was supported by the Kyungpook National University Research Fund , 2009. The fourth author’s research was supported in part by NSF grant DMS-1266016 . The research of the fifth author was partially supported by the Arnold O. Beckman Research Award of the University of Illinois at Urbana-Champaign.
PY - 2013
Y1 - 2013
N2 - We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: (3,3,∞), (3,4,11), (3,7,5), (3,10,4), (3,15,3), (4,4,9), (6,4,8), (7,4,7), and (6,5,6). No parameter of this description can be improved, as shown by appropriate 3-polytopes.
AB - We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: (3,3,∞), (3,4,11), (3,7,5), (3,10,4), (3,15,3), (4,4,9), (6,4,8), (7,4,7), and (6,5,6). No parameter of this description can be improved, as shown by appropriate 3-polytopes.
KW - Normal plane map 3-path
KW - Plane graph
KW - Structural property
KW - Weight
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U2 - 10.1016/j.disc.2013.08.018
DO - 10.1016/j.disc.2013.08.018
M3 - Article
AN - SCOPUS:84883484120
SN - 0012-365X
VL - 313
SP - 2702
EP - 2711
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 23
ER -