Combinatorics and Graph Theory: Reading Guide
Start with the lessons. Use MCS for the primary explanations and Rosen for targeted alternate examples. You do not need to read both books front-to-back. These links open book indexes; the locators below refer to the local chunk index, not guaranteed section numbering in every edition.
| After | MCS topic and local locator | Read-to-produce task |
|---|---|---|
| Counting models | Cardinality rules: 181–186 | A bijection and a uniform-fiber argument |
| Constraints | Pigeonhole 187–188; inclusion-exclusion 189 | An existence bound and a corrected overlap count |
| Recurrence/series | Counting with generating functions 201–202; linear recurrences 204; formal series 205 | A coefficient equation with initial corrections |
| Graph language | Simple graphs: degrees 137; isomorphism 139; walks/connectivity 144–145 | A precise model and a non-isomorphism witness |
| Trees | Forests and trees 148–149 | Leaf-removal proof and a forest edge count |
| Matching/coloring | Bipartite graphs and matchings 140–141; coloring 142–143 | A valid assignment and a deficient-neighborhood obstruction |
| Planarity | Planar definitions 160–161; Euler and edge bounds 162 | A plane-face proof with components and bridge boundaries |
Local roots are Books/Mathematics for Computer Science/contents/ and
Books/Discrete Mathematics and Its Applications/contents/, each with a README
index. Some extracted headings include material continued from previous sections;
verify the body and compare damaged symbols with the source PDF. Read a small
assigned topic, close the book, then reconstruct one argument.
Optional depth, each with a concrete output
- Broader problem selection: MIT 18.211, 2019 course gives a primary-source topic map spanning counting and graphs. Choose an exercise only after checking its prerequisites; record the exact course/assignment ID.
- Formal series: Stanley's author-hosted Enumerative Combinatorics volume 1 is an advanced reference. Use a specific formal-series question, not an additional required book. The whole text was not audited for this upgrade.
- Additional local books:
Resources/Catalogue-master/Discrete/contains Concrete Mathematics (Graham, Knuth, Patashnik), Combinatorics (Merris), and Combinatorics: Topics, Techniques and Algorithms (Cameron). These are located inventory candidates; no exact chapter assignment or full review is implied. Choose recurrence algebra, a counting proof or a graph topic for a named gap. - Graph depth:
Resources/pdfs/Graph Theory (2005).pdfis available; verify author/edition and contents before choosing a section. Produce a proof and a counterexample showing why one hypothesis is necessary.
Optional material adds time. For the full-book path, this assignment is a checkpoint in separately budgeted whole-book reading. The upgrade inspected selected local excerpts/indexes and targeted primary web sources; it did not audit every item in Books, reading or Resources.