http://blogs.springer.com/bondyandmurty The blog of the book by J.A. Bondy and U.S.R. Murty Mon, 05 Oct 2009 20:10:06 +0200 http://wordpress.org/?v=2.8.5 hourly 1 http://blogs.springer.com/bondyandmurty/?p=418&cpage=1#comment-2823 Adrian Bondy Mon, 05 Oct 2009 20:10:06 +0000 http://blogs.springer.com/bondyandmurty/?p=418#comment-2823 Yes, you're right. Thank you. Yes, you’re right. Thank you.

]]> http://blogs.springer.com/bondyandmurty/?p=414&cpage=1#comment-2822 Adrian Bondy Sun, 27 Sep 2009 21:22:29 +0000 http://blogs.springer.com/bondyandmurty/?p=414#comment-2822 Unsolved problem 70 is a special case of Thomassé's conjecture, which is stated as Conjecture 6.34. in the article by Blair Sullivan entitled "A summary of results and problems related to the Caccetta-Haggkvist Conjecture". The conjecture was mentioned at a workshop on the Caccetta-Haggkvist Conjecture held at the American Institute of Mathematics in early 2006. As Sullivan notes, it implies the Caccetta-Haggkvist Conjecture. For further information, you might contact Stephan Thomassé in Montpellier. Unsolved problem 70 is a special case of Thomassé’s conjecture, which is stated as Conjecture 6.34. in the article by Blair Sullivan entitled “A summary of results and problems related to the Caccetta-Haggkvist Conjecture”. The conjecture was mentioned at a workshop on the Caccetta-Haggkvist Conjecture held at the American Institute of Mathematics in early 2006. As Sullivan notes, it implies the Caccetta-Haggkvist Conjecture. For further information, you might contact Stephan Thomassé in Montpellier.

]]> http://blogs.springer.com/bondyandmurty/?p=397&cpage=1#comment-2821 Adrian Bondy Thu, 17 Sep 2009 09:16:44 +0000 http://blogs.springer.com/bondyandmurty/?p=397#comment-2821 It's the Turan graph (6,12), not (2,12). It has 2 x 30 = 60 edges, and is not bipartite. It’s the Turan graph (6,12), not (2,12). It has 2 x 30 = 60 edges, and is not bipartite.

]]> http://blogs.springer.com/bondyandmurty/?p=379&cpage=1#comment-2820 Adrian Bondy Wed, 02 Sep 2009 14:41:21 +0000 http://blogs.springer.com/bondyandmurty/?p=379#comment-2820 One can delete any leaf and use induction. One must show that the deleted vertex contributes exactly one additional uniform x-subtree. That subtree will necessarily contain all the children of the parent of x in the tree. One can delete any leaf and use induction. One must show that the deleted vertex contributes exactly one additional uniform x-subtree. That subtree will necessarily contain all the children of the parent of x in the tree.

]]> http://blogs.springer.com/bondyandmurty/?p=380&cpage=1#comment-2819 Adrian Bondy Wed, 02 Sep 2009 14:31:54 +0000 http://blogs.springer.com/bondyandmurty/?p=380#comment-2819 You are right. The equation should be w_n-w_{n-1}=f_{n+1}+f_n. (Perhaps we should have defined F_n to be the fan with n spokes.) You are right. The equation should be w_n-w_{n-1}=f_{n+1}+f_n.
(Perhaps we should have defined F_n to be the fan with n spokes.)

]]> http://blogs.springer.com/bondyandmurty/?p=376&cpage=1#comment-2818 Adrian Bondy Mon, 17 Aug 2009 22:47:59 +0000 http://blogs.springer.com/bondyandmurty/?p=376#comment-2818 This is true. One must apply Exercise 9.2.3 to A union C, where A is an appropriate subgraph of B, namely the union of all paths in B between pairs of vertices of attachment of B. This is true. One must apply Exercise 9.2.3 to A union C, where A is an appropriate subgraph of B, namely the union of all paths in B between pairs of vertices of attachment of B.

]]> http://blogs.springer.com/bondyandmurty/?p=369&cpage=1#comment-2817 Adrian Bondy Mon, 17 Aug 2009 22:30:32 +0000 http://blogs.springer.com/bondyandmurty/?p=369#comment-2817 Also, it should be assumed that G is 2-connected. Also, it should be assumed that G is 2-connected.

]]> http://blogs.springer.com/bondyandmurty/?p=171&cpage=1#comment-1449 Adrian Bondy Tue, 17 Feb 2009 22:18:29 +0000 http://blogs.springer.com/bondyandmurty/?p=171#comment-1449 Thanks for pointing out that the formula was inadvertently truncated in the hint (though not in the exercise itself). This has now been corrected. As regards your second remark, this is not a problem: please note the ceiling function in the upper bound on the chromatic number. Thanks for pointing out that the formula was inadvertently truncated in the hint (though not in the exercise itself). This has now been corrected. As regards your second remark, this is not a problem: please note the ceiling function in the upper bound on the chromatic number.

]]> http://blogs.springer.com/bondyandmurty/?p=171&cpage=1#comment-1448 vcolor Tue, 17 Feb 2009 20:16:32 +0000 http://blogs.springer.com/bondyandmurty/?p=171#comment-1448 Hint to exercise 14.1.10.b is broken. Summation over degrees given an extra $-k$? Hint to exercise 14.1.10.b is broken. Summation over degrees given an extra $-k$?

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