Structure of Graphs (TAC: Vol. II) - Typos
This page lists the errors that have been discovered in the Spring 2012
pre-publication version of Structure of Graphs, by Douglas B. West
(Volume II of The Art of Combinatorics).
This page is of interest only to the few persons having a copy of this
draft, such as the students in Math 582 and possibly reviewers.
Please send any additional contributions to west@math.uiuc.edu.
Contributors noted in parentheses.
Category 1: Notational typos and other Mathematical Corrections
- p50 - after Definition 6.1.38: every T in this paragraph should be
H (Tom Mahoney)
- p60 - Case 1: The statement about numbering the accessible non-free classes
is not true. Fortunately, only a weaker statement is needed; that we can let
Vi be such a class that blocks only free classes.
- p131 - before Lemma 6.4.25: "edge-colorings number" should be "the
edge-chromatic number"
- p140 - Example 7.1.3: The labeling of the figure doesn't agree with the
text. Vertex i should be made adjacent to i+(n-1)/2; we don't
want edges to have "length" exceeding n/2 (Greg Puleo)
- p182 - Exercise 7.1.67: In the conclusion of part (b), "2k" should
be "3k"
Category 2: Other Changes, Comments and Corrections of Note
- p53 - Examples 6.1.47-48: This material has been replaced by the
construction by Maheo in order to give a complete proof that hypercubes have
up/down labelings
- p57 - Example 6.1.58: It should be noted that the case d1
is the sharpness example of Theorem 6.1.57
- p58 - after Conjecture 6.1.59: The statement about ε=.1168 is
obsolete; it came from an early draft of the Kaul-Kostochka paper and was
never published. What was published was ε=.2 in the Kaul-Kostochka-Yu
paper.
- p93 - Exercise 6.2.43: The reference to Dirac's Theorem should be to
Corollary 7.3.12
- p179 - Exercise 7.1.42: The reference to Exercise 7.1.42 should be to
"part (a)".
- p180 - Exercises 7.1.56-57 repeat Exercises 6.2.49-50 and have been
deleted
- p180 - Exercises 7.2.23-24 repeat Exercises 6.2.14 and 16 and have been
deleted
Category 3: Minor Changes, Typos, and Clarifications
- p42 - Proof of Corollary 6.1.19: "called called" should be "called" (Ali
Vakilian)
- p55 - Theorem 6.1.52: "a 2-factors" should be "a 2-factor" (Mike Santana).
Also, "because if it did" should be "because if so"
- p59 - After Example 6.1.59: "divides the |V(G)|" should be
"divides |V(G)|"
- p93 - Exercises 6.2.40: "that then the" should be "that the"
- p112 - near bottom: "finite many trees" should be "finitely many trees"