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Degeneracy of graph

Degeneracy of outerplanar graphsSubgraph without “holes”Can deleting an edge from a graph create a single subgraph?Density of Subgraphstreewidth and a complete k-vertex SubgraphProve that this graph is nonplanarDefinition: is a graph allowed to have a “dangling” edge without a vertex at its end(s)?Reference request: Concerning a connectivity property of a graphThe Wikipedia definition of the degeneracy of a graph.Is “induced subgraph” necessary to define an $H$-free graph?

0

$begingroup$

I'm not really sure I get what the degeneracy of a graph is. My book gives the following definition:

$δ^*(G)=max$ such that there is a subgraph Η of G: $δ(H)geq k$

Does that imply that $δ^*(G)$ is the supremum of the set containing the minimum vertex degree for all the possible subgraphs of $G$?

And also how do I find the degeneracy of a graph in general?

For example the book gives this excerisise:

Find the value of $δ^*(G) (barK_1,q ∗ barK_1,r),$ $q,r geq1$

The definition doesn't seem very usefull here..

Also do you know any free online books on introduction to graph theory? I just don't think mine is good enough

graph-theory

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asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

$endgroup$

add a comment | 

0

$begingroup$

I'm not really sure I get what the degeneracy of a graph is. My book gives the following definition:

$δ^*(G)=max$ such that there is a subgraph Η of G: $δ(H)geq k$

Does that imply that $δ^*(G)$ is the supremum of the set containing the minimum vertex degree for all the possible subgraphs of $G$?

And also how do I find the degeneracy of a graph in general?

For example the book gives this excerisise:

Find the value of $δ^*(G) (barK_1,q ∗ barK_1,r),$ $q,r geq1$

The definition doesn't seem very usefull here..

Also do you know any free online books on introduction to graph theory? I just don't think mine is good enough

graph-theory

share|cite|improve this question

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

$endgroup$

add a comment | 

$begingroup$

I'm not really sure I get what the degeneracy of a graph is. My book gives the following definition:

$δ^*(G)=max$ such that there is a subgraph Η of G: $δ(H)geq k$

Does that imply that $δ^*(G)$ is the supremum of the set containing the minimum vertex degree for all the possible subgraphs of $G$?

And also how do I find the degeneracy of a graph in general?

For example the book gives this excerisise:

Find the value of $δ^*(G) (barK_1,q ∗ barK_1,r),$ $q,r geq1$

The definition doesn't seem very usefull here..

Also do you know any free online books on introduction to graph theory? I just don't think mine is good enough

graph-theory

share|cite|improve this question

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

$endgroup$

share|cite|improve this question

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

share|cite|improve this question

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998

asked Mar 28 at 16:22

VakiPitsiVakiPitsi

1998