Send contributions of errors, comments, or supplementary problems to dwest@illinois.edu; contributors noted in parentheses. Locating codes: X=Exercise, T=Theorem, L=Lemma, P=Proposition, C=Corollary, E=Example, J=Conjecture. $ \def\nul{\emptyset}\def\NN{{\bf N}}\def\ZZ{{\bf Z}}\def\RR{{\bf R}} \def\FL#1{\lfloor{#1}\rfloor}\def\CL#1{\lceil{#1}\rceil} \def\C#1{\left|{#1}\right|} \def\esub{\subseteq} \def\FR#1#2{{{#1}\over{#2}}} \def\st{\colon\,} \def\join{\vee} \def\Sb{\overline{S}} \def\cart{\square} \def\CH#1#2{{#1\choose #2}} \def\XPOL#1#2{\chi_{#1}(#2)} \def\VEC#1#2#3{#1_{#2},\ldots,#1_{#3}} \def\D{{\diamond}} $

- p133 X3.3.21: In part (b), the factor "$i^{\FL{m/i}}$" should be "$i^{\FL{m/(i-1)}}$".
- p235 X5.3.3: Part (c) is ambiguously stated. It was intended to be "For each vertex $v$ in a circuit, the circuit contains a cycle through $v$", without requiring a single cycle through all the vertices (containment is in the sense of Lemma 5.3.8).

- p249 X5.4.27: The problem of finding the largest $f(n)$ such that some $n$-vertex graph with $n+f(n)$ edges has no two cycles with the same length was originally posed by Erdős in 1975. Shi [1988] proved roughly $f(n)\ge\sqrt{2n-4}$. The CM text mis-states the result of Chen-Lehel-Jacobson-Shreve [1988], which is $f(n)\le O(\sqrt{n\log n})$ (also proved earlier in Lai [1990]). Lai [2020] improved the lower bound to $f(n)\ge 1.55\sqrt n$, and Boros-Caro-Füredi-Yuster [2001] proved $f(n)\le 1.98\sqrt n$. The restriction of the problem to $2$-connected graphs has been solved asymptotically; the number of edges is $n+f_2(n)$ where $f_2(n)\sim \sqrt{n}$. The lower bound is in Boros-Caro-Füredi-Yuster [2001], upper bound in Ma-Yang [2020+]. (Chunhui Lai)

- p114 X3.2.12 and p116 X3.2.33: Unfortunately, these two are the same exercise, in slightly different notation.
- p128 X3.2.28: An excellent exercise; should be marked ($\D$). There should be a hint in the back reminding solvers to be careful about which square root of $(1-2p)^2$ makes sense. With this, the computations in parts (a) and (b) both work out nicely for the relevant values of $p$. (Kevin Milans)
- p150 X3.4.26: This problem is worthy of ($\D$).
- p207-208 X4.3.13,19,20: These ($\D$) exercises are fairly long.
- p228 X5.2.34 and p255 C6.1.5: A proof of C6.1.5 by directly improving a given orientation is requested in X5.2.34.
- p273 X6.2.20: There is nice non-inductive proof using augmenting paths.
- p297 X7.1.25: Parts (a) and (b) are suitable exercises separately.

Additional exercises will be listed here as collected. Suggestions welcome.