Caro et al. proved that every tree of order n contains an induced subgraph of order at least rn/2] with all degrees odd, and conjectured a better bound. In this note we prove that every tree of order n contains an induced subgraph of order at least 2L(n + 1)/3 .] with all degrees odd; this bound is
On induced subgraphs with odd degrees
β Scribed by Yair Caro
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 336 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Solving a problem of Alon, we prove that every graph G on n vertices with 6(G) 2 1 contains an induced subgraph H such that all the degrees in H are odd and 1 V(H)\ >(l -o(l))Jn/6.
π SIMILAR VOLUMES
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Graphs with n + k vertices in which every set of n +j vertices induce a subgraph of maximum degree at least n are considered. For j = 1 and for k fairly small compared to n, we determine the minimum number of edges in such graphs.
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