# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Mon, 20 May 2013 03:56:24 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 5 posts ]
 Print view Previous topic | Next topic
Author Message
 S.O.S. Newbie

Joined: Wed, 6 Apr 2011 10:17:04 UTC
Posts: 1

1) Prove that if G is a graph with vertices with minimum degree bigger or equal to two, then G contains a cycle.

2) Prove that every graph G has a path of length equal to the minimum degree of all its vertices.

Any assistance would be appreciated.

Top

 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6005
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Elesar wrote:

1) Prove that if G is a graph with vertices with minimum degree bigger or equal to two, then G contains a cycle.

2) Prove that every graph G has a path of length equal to the minimum degree of all its vertices.

Any assistance would be appreciated.

(1) Really? What about and ?

(2) Construct such a path.

_________________

Top

 S.O.S. Oldtimer

Joined: Sat, 16 Aug 2008 04:47:19 UTC
Posts: 208
outermeasure wrote:
Elesar wrote:

1) Prove that if G is a graph with vertices with minimum degree bigger or equal to two, then G contains a cycle.

(1) Really? What about and ?

Sometimes a graph, perhaps in the context of this OP, is considered to only be referring to a finite number of vertices.

Top

 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
daveyinaz wrote:
outermeasure wrote:
Elesar wrote:

1) Prove that if G is a graph with vertices with minimum degree bigger or equal to two, then G contains a cycle.

(1) Really? What about and ?

Sometimes a graph, perhaps in the context of this OP, is considered to only be referring to a finite number of vertices.

Perhaps, but perhaps not. He needs to say something to that end if that's what he means.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Posted: Fri, 8 Apr 2011 04:13:48 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632
Most applications involve a finite number of vertices. Only research mathematicians would consider infinitely many, so we should always consider the finite case as primary on the Cyberboard.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 5 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous