## Abstract Let __G__ be a connected graph of order __p__ ≥ 2, with edge‐connectivity κ~1~(__G__) and minimum degree δ(__G__). It is shown her ethat in order to obtain the equality κ~1~(__G__) = δ(__G__), it is sufficient that, for each vertex __x__ of minimum degree in __G__, the vertices in the n
A minimum degree condition forcing complete graph immersion
✍ Scribed by Devos, Matt; Dvořák, Zdeněk; Fox, Jacob; McDonald, Jessica; Mohar, Bojan; Scheide, Diego
- Book ID
- 121555525
- Publisher
- Springer-Verlag
- Year
- 2014
- Tongue
- English
- Weight
- 420 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0209-9683
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## Abstract For a graph __G__, let __n__(__G__), κ(__G__) and δ(__G__) denote the order, the connectivity, and the minimum degree of __G__, respectively. The paper contains some conditions on __G__ implying κ(__G__) = δ(__G__). One of the conditions is that __n__(__G__) ≤ δ(__G__)(2__p__ −1)/(2__p_
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