TY - JOUR

T1 - Tight Descriptions of 3-Paths in Normal Plane Maps

T2 - Dedicated to Andre Raspaud on the occasion of his 70th birthday

AU - Borodin, O. V.

AU - Ivanova, A. O.

AU - Kostochka, A. V.

N1 - Publisher Copyright:
© 2016 Wiley Periodicals, Inc.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We prove that every normal plane map (NPM) has a path on three vertices (3-path) whose degree sequence is bounded from above by one of the following triplets: (3, 3, ∞), (3,15,3), (3,10,4), (3,8,5), (4,7,4), (5,5,7), (6,5,6), (3,4,11), (4,4,9), and (6,4,7). This description is tight in the sense that no its parameter can be improved and no term dropped. We also pose a problem of describing all tight descriptions of 3-paths in NPMs and make a modest contribution to it by showing that there exist precisely three one-term descriptions: (5, ∞, 6), (5, 10, ∞), and (10, 5, ∞).

AB - We prove that every normal plane map (NPM) has a path on three vertices (3-path) whose degree sequence is bounded from above by one of the following triplets: (3, 3, ∞), (3,15,3), (3,10,4), (3,8,5), (4,7,4), (5,5,7), (6,5,6), (3,4,11), (4,4,9), and (6,4,7). This description is tight in the sense that no its parameter can be improved and no term dropped. We also pose a problem of describing all tight descriptions of 3-paths in NPMs and make a modest contribution to it by showing that there exist precisely three one-term descriptions: (5, ∞, 6), (5, 10, ∞), and (10, 5, ∞).

KW - 3-path

KW - normal plane map

KW - plane graph

KW - structural property

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U2 - 10.1002/jgt.22051

DO - 10.1002/jgt.22051

M3 - Article

AN - SCOPUS:84978237208

SN - 0364-9024

VL - 85

SP - 115

EP - 132

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 1

ER -