Graph Theory: 42. Degree Sequences and Graphical Sequences

Here I describe what a degree sequence is and what makes a sequence graphical. Using some examples I'll describe some obvious necessary conditions (which are not sufficient). Then I explain how a Theorem by Havel and Hakimi gives a necessary and sufficient condition for a sequence of non-negative integers to be graphical and show how the theorem can be used repeatedly as an algorithm to determine this. The proof of this theorem will be provided in the next video.
--Bits of Graph Theory by Dr. Sarada Herke.
Links to the related videos:
• Graph Theory: 05. Conn... - Graph Theory: 05. Connected and Regular Graphs
• Graph Theory: 10. Isom... - Graph Theory: 10. Isomorphic and Non-Isomorphic Graphs
• Graph Theory: 06 Sum o... - Graph Theory: 06 Sum of Degrees is ALWAYS Twice the Number of Edges
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