Journal
EUROPEAN JOURNAL OF COMBINATORICS
Volume 75, Issue -, Pages 1-10Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ejc.2018.07.010
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Funding
- NSF [DMS-1700157]
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We prove two results: 1. A graph G on at least seven vertices with a vertex v such that G - v is planar and t triangles satisfies vertical bar E(G)vertical bar <= 3 vertical bar V(G)vertical bar - 9 + t/3. 2. For p = 2, 3, ... , 9, a triangle-free graph G on at least 2p-5 vertices with no K-p-minor satisfies vertical bar E(G)vertical bar <= (p - 2)vertical bar V(G)vertical bar - (p - 2)(2). (C) 2018 The Authors. Published by Elsevier Ltd. All rights reserved.
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