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Graphs with given odd sets and the least number of vertices

✍ Scribed by Louis Hakimi, S.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 64 KB
Volume: 24
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199701)24:1<81::aid-jgt9>3.0.co;2-f

No coin nor oath required. For personal study only.

✦ Synopsis

This note presents a solution to the following problem posed by Chen, Schelp, and Soltés: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given.

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## Abstract For a vertex __v__ of a graph __G__, we denote by __d__(__v__) the __degree__ of __v__. The __local connectivity__ κ(__u, v__) of two vertices __u__ and __v__ in a graph __G__ is the maximum number of internally disjoint __u__ –__v__ paths in __G__, and the __connectivity__ of __G__ is