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On the Edge Reconstruction of Graphs Embedded in Surfaces II
Author(s) -
Zhao Yue
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798005924
Subject(s) - mathematics , combinatorics , graph , enhanced data rates for gsm evolution , surface (topology) , degree (music) , discrete mathematics , geometry , computer science , artificial intelligence , physics , acoustics
In this paper, we prove the following theorems. (i) Let G be a graph of minimum degree δ⩾5. If G is embeddable in a surface σ and satisfies (δ−5)∣ V ( G )∣+6χ(Σ)⩾0, then G is edge reconstructible. (ii) Any graph of minimum degree 4 that triangulates a surface is edge reconstructible. (iii) Any graph which triangulates a surface of characteristic χ⩾0 is edge reconstructible.