# Structure of Graphs (TAC: Vol. II)'' - Typos

This page lists the errors that have been discovered in the Spring 2008 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

• p76, Lemma 6.2.11: There are some mixups between q and t
• p82, Example 6.2.23: "G" should be "H"
• p158, Remark 7.1.57: In the last paragraph, the join should be with K2, not 2K1 (also in Exercise 70)
• p184, Lemma 7.2.15: at the end of the first paragraph, "y,N(z)-fan" is wrong. It should be a "w,{x,y,z}-fan", where w is chosen outside {x,y,z} (Kyle Jao)
• p184, Theorem 7.2.16: x1 and x2 should be switched beginning with "when e=x2x3" (Kyle Jao)
• p187, Lemma 7.2.18: "neighors" should be "neighbors", and there cardinality signs missing in an inequality near the end of the proof
• p194-5: "minimal 2k-edge-connected" should be "minimally 2k-edge-connected" throughout this discussion (Kyle Jao)
• p261, Theorem 8.1.41: In the discussion of J, the appearances of G should be J
• p310, Lemma 8.2.32: "components" should be "blocks"
• p335, Theorem 8.3.11: It is simpler to apply the argument to all the cycles in the symmetric difference of M with any arbitrary matching. The description of C needs to be clarified
• p327, Definition 8.3.1: parenthesis missing at end
• p329, Lemma 8.3.3: "x,y-path" should be "x,z-path"
• p330, Theorem 8.3.5: "3n" should be "8n"
• p336, Theorem 8.3.12: There are various words missing in the proof.
• p337, Theorem 8.3.13: "Also traverse" should be "Also C traverses".
• p375, Corollary 8.5.8: "e-2n" should be "m-2n"
• p381, Theorem 8.5.19: "2e/n" should be "2m/n"
• p418, Exercise 9.1.6: The upper bound must be larger by 1

## Category 2: Other Changes, Comments and Corrections of Note

• p330-332: The discussion of the Separator Theorem and its applications looks less formidable with 2\sqrt{2n} changed to \sqrt{8n}.

## Category 3: Minor Changes, Typos, and Clarifications

• p61, Exercise 6.1.15: space missing before first e1
• p61, Exercise 6.1.17: first letter of "threshold" missing
• p297, Theorem 8.2.17: for 6-vertices, "not charge" should be "no charge"
• p312, Lemma 8.2.37: "illustrate beloe" should be "illustrated below"
• p347, Exercise 8.3.9: "perfact" should be "perfect"
• p355, Remark 8.4.11: "Pelsmaje" should be "Pelsmajer"
• p358, Example 8.4.18: the vertices along the horizontal axis should be split using the floor and ceiling of r/2
• p398, above Theorem 9.1.4: "an edges" should be "an edge"
• p401, above Definition 9.1.10: "r-1-colorable" should be "(r-1)-colorable"