| Stars and bars | 009TEMTQKH | statement | 05A10 |
| Graph | 00C0BR7D7H | concept | 05C99 |
| Graph isomorphism | 00CT0PTH74 | definition | 05C60 |
| Multinomial coefficient | 00K0RF9BFY | definition | 05A10 |
| Ramsey's theorem | 00TQV3F5S4 | statement | 05D10, 05C55 |
| Dyck words are counted by Catalan numbers | 017SRZ7NE9 | statement | 05A15 |
| Ramsey number | 01DSVCRF6X | definition | 05C55, 05D10 |
| Vandermonde's identity | 01JADB9VW5 | statement | 05A19 |
| Multigraph | 01M5T0KDG7 | definition | 05C99 |
| Sum of the first n natural numbers | 01QZNHQWYD | statement | 05A19 |
| A graph is bipartite iff it has no odd cycle | 01R1HPEK6S | statement | 05C75 |
| Neighbourhood | 01T3TMGTTE | definition | 05C07 |
| Connected component | 01VVP10MWJ | definition | 05C40 |
| Central binomial coefficient | 01WHD9T0V6 | definition | 05A10 |
| Euler's theorem on Eulerian circuits | 020422MDQF | statement | 05C45 |
| Planar graph | 029JQEK15B | definition | 05C10 |
| Binary tree | 02A8EMC83C | definition | 05C05 |
| Edge colouring | 02CDYWSWSY | definition | 05C15 |
| K5 and K3,3 are not planar | 030A3FHN14 | statement | 05C10 |
| Factorial formula for binomial coefficients | 033KTKKRV6 | statement | 05A10 |
| Chromatic polynomial | 038YGY0HSC | definition | 05C31, 05C15 |
| Path | 03NAMV1DHJ | concept | 05C38 |
| Complement principle | 03QC59M99B | statement | 05A05 |
| Formula for the number of derangements | 03RSJXF728 | statement | 05A05 |
| Complete graph | 03WKB2H474 | example | 05C99 |
| Number of derangements | 03WY4HHMT1 | definition | 05A05 |
| Sum of a finite geometric progression | 03X8V7D64M | statement | 05A19 |
| Integer partition | 0404R9P9J3 | definition | 05A17 |
| Lattice path | 040WY0TT2G | concept | 05A15 |
| The derangement numbers count derangements | 045ENVCCZV | statement | 05A05 |
| Greedy colouring | 04AAKZNXHD | concept | 05C15 |
| Hockey-stick identity | 04JHQNNBFE | statement | 05A19 |
| Clique number | 04MQSQ1F5Q | concept | 05C69 |
| Every connected graph has a spanning tree | 04XPQT2XTC | statement | 05C05 |
| Graph homomorphism | 052JJ9YVNM | concept | 05C60 |
| Number of compositions | 057H72B2MB | statement | 05A17 |
| Pascal's triangle | 05DME4TZ3K | object | 05A10 |
| Eulerian trail | 05NWGBHKSZ | concept | 05C45 |
| Number of edges of a complete graph | 05RN90E14Y | statement | 05C30 |
| Permutation | 05RWFKVTJ7 | concept | 05A05 |
| Number of derangements | 05WR29H2KH | concept | 05A05 |
| Perfect matching | 05ZPH8KF9K | definition | 05C70 |
| Tree | 062D9KXJB1 | concept | 05C05 |
| Trail | 062MQGP8M5 | definition | 05C38 |
| Five colour theorem | 06C0JBE52D | statement | 05C15, 05C10 |
| Symmetric polynomial | 06CTFY2DEZ | definition | 05E05 |
| Graph homomorphism | 06SCB3R6BN | definition | 05C60 |
| Path graph | 075WR6W3Y3 | example | 05C38 |
| Cycle | 07CT9RDY7Q | definition | 05C38 |
| Bipartite graph | 07DVHJ8N0A | definition | 05C75 |
| Walk | 085CH3CYMX | concept | 05C38 |
| Graph colouring | 0874138YP6 | definition | 05C15 |
| Independent set | 08ANQHHG3P | concept | 05C69 |
| Adjacency matrix | 08B9CX109G | concept | 05C50 |
| Tutte's theorem | 08J7R35B6Q | statement | 05C70 |
| Number of functions between finite sets | 08QQH9F7G0 | statement | 05A05 |
| Permutation matrix | 08SP3DF8NB | concept | 15A99, 05A05 |
| Hall's marriage theorem | 08WCB90WND | statement | 05D15 |
| Hamiltonian graph | 090WPKFABX | definition | 05C45 |
| Catalan numbers | 092DRBFKMG | definition | 05A15 |
| Binomial coefficient | 092GEF38YD | definition | 05A10 |
| Young diagram | 096AHMB3P4 | concept | 05A17 |
| Unique paths in trees | 096B7Q5742 | statement | 05C05 |
| Combination | 098PHYBTV9 | concept | 05A05 |
| Circuit | 09F2QPVQY7 | concept | 05C38 |
| Forest | 09JP6G9FTA | definition | 05C05 |
| Prüfer sequence | 09PV9JSY6E | definition | 05C05 |
| Every walk contains a path | 09VZBHB33V | statement | 05C38 |
| Vertex cover | 0AHKWBQSWV | concept | 05C70, 05C69 |
| Edge set | 0AQBSVMX9P | concept | 05C99 |
| Power sum symmetric polynomials | 0AS1FZT6BM | definition | 05E05 |
| Edge colouring | 0B5WCC02AN | concept | 05C15 |
| Chromatic polynomial | 0B621RBVS9 | concept | 05C31, 05C15 |
| Bridge | 0BANA3XYPF | concept | 05C40 |
| Number of k-element subsets | 0BFMR2FQ8B | statement | 05A10 |
| Trees are bipartite | 0BN2A6EBYA | statement | 05C05 |
| Permutation | 0BQMWCNS8S | definition | 05A05 |
| Generalized pigeonhole principle | 0BY7GN3449 | statement | 05A05 |
| Clique | 0BYX1D7C2E | concept | 05C69 |
| Inclusion–exclusion for two sets | 0C4YEQ9H5E | statement | 05A05 |
| Chromatic number | 0C5M7AM6FH | definition | 05C15 |
| Number of subsets of a finite set | 0C5RDJE73X | statement | 05A05 |
| Multigraph | 0C62PZXX02 | concept | 05C99 |
| Rooted tree | 0C9J6W2A8A | definition | 05C05 |
| Degrees along an Eulerian trail | 0CDVDGWGEG | statement | 05C45 |
| Number of permutations | 0CEBCS0E0E | statement | 05A05 |
| Binary tree | 0D7EZ10V2R | concept | 05C05 |
| Bridge | 0D81KWH9ZM | definition | 05C40 |
| Rule of sum | 0EE2V3CHFK | statement | 05A05 |
| Binomial theorem | 0EHWPWGHB2 | statement | 05A10 |
| Induced subgraph | 0EREPBVG2G | concept | 05C99 |
| Graph isomorphism | 0F7QKGJS6B | concept | 05C60 |
| Double counting | 0F8YBHF2W3 | concept | 05A19 |
| Reachability | 0FDKRX9M9Y | concept | 05C40 |
| Inclusion–exclusion principle | 0FF7726C7P | statement | 05A05 |
| Connected graph | 0FFAYNMAJZ | definition | 05C40 |
| Characterization of bridges | 0FHM8DB6PM | statement | 05C40 |
| Chromatic number of a complete bipartite graph | 0FJBBCXYPS | statement | 05C15 |
| Maximum degree | 0FJY6G7FNA | concept | 05C07 |
| Spanning tree | 0FQ5B8S1ZC | definition | 05C05 |
| Infinite pigeonhole principle | 0FS3RHF6KE | statement | 05A05 |
| Bertrand's ballot theorem | 0FS972T0ZH | statement | 05A15 |
| Clique | 0G52BPNPKG | definition | 05C69 |
| Binomial coefficient | 0GBZM0MT0F | concept | 05A10 |
| Prüfer sequence | 0GDQRETR59 | concept | 05C05 |
| Forest | 0GGXWDNKBR | concept | 05C05 |
| Bijection principle | 0GV2573FP4 | statement | 05A19 |
| Fundamental theorem of symmetric polynomials | 0GW1ZZH0R4 | statement | 05E05 |
| Cayley graph | 0GYQK9NDJF | concept | 05C25, 20F65 |
| Every finite tree with at least two vertices has a leaf | 0H8Q4MANBD | statement | 05C05 |
| Hamiltonian cycle | 0HF30P75G4 | concept | 05C45 |
| Pigeonhole principle | 0HGVCWQGY3 | statement | 05A05 |
| Generating function | 0HH6JX5WZZ | definition | 05A15 |
| Hamiltonian cycle | 0HKXNG2RS1 | definition | 05C45 |
| Hamiltonian graph | 0HYV2NME07 | concept | 05C45 |
| Kuratowski's theorem | 0J6G5NJC5R | statement | 05C10 |
| Sperner's theorem | 0J87V9K1GE | statement | 05D05 |
| Composition of an integer | 0J8ANSYKAC | definition | 05A17 |
| Reachability | 0J8XE7W68F | definition | 05C40 |
| Graph | 0JD5C82QMB | definition | 05C99 |
| Path | 0JDE56HWQ8 | definition | 05C38 |
| Turán's theorem | 0JG1KZSPFZ | statement | 05C35 |
| Connected component | 0JG9W3KA6B | concept | 05C40 |
| Exponential generating function | 0JHXPVFKT0 | concept | 05A15 |
| Combinatorics | 0JKW7W7XFR | concept | 05A99 |
| Kőnig's theorem | 0JP0ZF57PN | statement | 05C70 |
| Central binomial coefficient | 0JPH2Y4DFV | concept | 05A10 |
| Integer partition | 0JV30XN73Z | concept | 05A17 |
| Minimum spanning tree | 0JW7KT6PQW | concept | 05C05 |
| Combination | 0JZSRWRBZE | definition | 05A05 |
| Young diagram | 0K78D81EF7 | definition | 05A17 |
| Ramsey number | 0K9QVPJYJF | concept | 05C55, 05D10 |
| Regular graph | 0KA4S8R39M | definition | 05C07 |
| Sum of binomial coefficients | 0KAMF19NV8 | statement | 05A10 |
| Stirling's formula | 0KC0F51T6A | statement | 41A60, 05A10 |
| Vertex cover | 0KDADE9RQ8 | definition | 05C70, 05C69 |
| Exponential generating function | 0KE6NBTVY8 | definition | 05A15 |
| Directed graph | 0KFYGSHHF5 | concept | 05C20 |
| Maximum degree | 0KNAN9F27P | definition | 05C07 |
| Degree of a vertex | 0KS0KRDV4Y | concept | 05C07 |
| Connected graph | 0KWFFMDF8T | concept | 05C40 |
| Independent set | 0KZJ82WEPP | definition | 05C69 |
| Cayley's formula | 0M2SSGSYPE | statement | 05C30 |
| Four colour theorem | 0M406JC8J1 | statement | 05C15, 05C10 |
| Complement graph | 0MCYJ72VGA | concept | 05C76 |
| Matching | 0MJ04A50QW | concept | 05C70 |
| Tree | 0MJ0JS72DZ | definition | 05C05 |
| Mantel's theorem | 0MXEHSCYCS | statement | 05C35 |
| Falling factorial | 0N5M924N3P | definition | 05A10 |
| Ore's theorem | 0NACHJYPKW | statement | 05C45 |
| Planar graph | 0NC9R64TXP | concept | 05C10 |
| Graph colouring | 0NCPXH194Y | concept | 05C15 |
| Perfect matching | 0NHK9MFFW9 | concept | 05C70 |
| Closed formula for Catalan numbers | 0NNDQVJ54Q | statement | 05A15 |
| Eulerian trail | 0NNYDD1AVR | definition | 05C45 |
| Petersen graph | 0NR95CTFCZ | example | 05C99 |
| Theorem on friends and strangers | 0NYM0ZGAK9 | statement | 05C55, 05D10 |
| Adjacency matrix | 0NZ8MDBN6Q | definition | 05C50 |
| Subgraph | 0P11X5HKAX | definition | 05C99 |
| Composition of an integer | 0P7FZHXZ5S | concept | 05A17 |
| Multinomial coefficient | 0PCV9EDJM2 | concept | 05A10 |
| Circuit | 0PD57PSHNR | definition | 05C38 |
| Generating function | 0PHAC833JF | concept | 05A15 |
| Alternating sum of binomial coefficients | 0PQQGFAWSH | statement | 05A10 |
| Permutation matrix | 0Q5SM60HTH | definition | 15A99, 05A05 |
| Regular graph | 0Q70YFB6ZM | concept | 05C07 |
| Cycle graph | 0QQ0F12962 | example | 05C38 |
| Number of odd-degree vertices is even | 0QQQQCPZA8 | statement | 05C07 |
| Recurrence for derangements | 0QRRYXG7V7 | statement | 05A05 |
| Distance in a graph | 0QV9VNNB4Z | concept | 05C12 |
| Directed graph | 0R5HTV7REV | definition | 05C20 |
| Symmetry of binomial coefficients | 0R7JS3DP3W | statement | 05A10 |
| Complement graph | 0RNMP6VCR2 | definition | 05C76 |
| Spanning tree | 0S4ZEZM7KE | concept | 05C05 |
| Falling factorial | 0SJNCJCCQG | concept | 05A10 |
| Edge bound for planar graphs | 0SM1REAVYJ | statement | 05C10 |
| Erdős–Szekeres theorem | 0SNJM8HSD3 | statement | 05A05 |
| Acyclic graph | 0SXHBTNM9T | concept | 05C05 |
| Degree of a vertex | 0T0F6CCS9W | definition | 05C07 |
| Dirac's theorem on Hamiltonian cycles | 0TC99BRSSB | statement | 05C45 |
| Derangement | 0TH61JR04G | definition | 05A05 |
| Minimum degree | 0TKZCSGCCA | definition | 05C07 |
| Induced subgraph | 0V05FC4GKQ | definition | 05C99 |
| Complete bipartite graph | 0V0GC7BQAN | example | 05C99 |
| Chromatic number | 0VHJRXNAAS | concept | 05C15 |
| Symmetric polynomial | 0VHSHB9B6J | concept | 05E05 |
| Walk | 0VJZM0F9YM | definition | 05C38 |
| Rule of product | 0VPK4X73Q0 | statement | 05A05 |
| Combinations with repetition | 0VQQCVG8WA | concept | 05A10 |
| A tree on n vertices has n − 1 edges | 0VSNHTHK8T | statement | 05C05 |
| Turán graph | 0VTCABADBE | example | 05C35 |
| Euler's formula for planar graphs | 0W1C598HMS | statement | 05C10 |
| Trail | 0W50MT1C6X | concept | 05C38 |
| Subgraph | 0WBFFC8XZ9 | concept | 05C99 |
| Clique number | 0WCKRBHFFD | definition | 05C69 |
| Factorial | 0WFCGVMRRC | definition | 05A10 |
| Newton's identities | 0WG2A3HE0S | statement | 05E05 |
| Edge set | 0WNGQBPPQX | definition | 05C99 |
| Distance in a graph | 0WPZ5YPAGR | definition | 05C12 |
| Number of injections | 0X0N833FF8 | statement | 05A05 |
| Hall's theorem for bipartite graphs | 0X2GJPNPFN | statement | 05C70 |
| Elementary symmetric polynomial | 0X5QVCF06N | concept | 05E05 |
| Handshaking lemma | 0XAP8WHNES | statement | 05C07 |
| Multinomial theorem | 0XFC1VQYEK | statement | 05A10 |
| Euler's partition theorem | 0XFZ1BMF5Q | statement | 05A17 |
| Derangement | 0XHWTD3MPV | concept | 05A05 |
| K-colourable graph | 0XHZW0VCPR | concept | 05C15 |
| Acyclic graph | 0XNN9Z8E5A | definition | 05C05 |
| Factorial | 0XWG0JGDFW | concept | 05A10 |
| Rooted tree | 0Y0JGC2K9T | concept | 05C05 |
| Catalan recurrence | 0Y1MG9R5VN | statement | 05A15 |
| Brooks' theorem | 0Y4TV2D5RQ | statement | 05C15 |
| K-colourable graph | 0Y7VDAX8Q3 | definition | 05C15 |
| Binary trees are counted by Catalan numbers | 0Y97E2DMB7 | statement | 05C05 |
| Seven Bridges of Königsberg | 0YCW781Q9D | example | 05C45 |
| Cayley graph | 0YE597NHGB | definition | 05C25, 20F65 |
| Combinations with repetition | 0YEQG3VBYC | definition | 05A10 |
| Pascal's rule | 0YRG241HQQ | statement | 05A10 |
| Catalan numbers | 0YWZJEABB2 | concept | 05A15 |
| Cycle | 0Z05VCBQ7Y | concept | 05C38 |
| Minimum spanning tree | 0Z367CGNRM | definition | 05C05 |
| Burnside's lemma | 0Z47M1B2VS | statement | 20B05, 05E18 |
| Matching | 0Z87BHAFTB | definition | 05C70 |
| Neighbourhood | 0ZCY0Z80B6 | concept | 05C07 |
| Minimum degree | 0ZFZ8ZG3EN | concept | 05C07 |
| Elementary symmetric polynomials | 0ZMY8441GW | definition | 05E05 |
| Power sum symmetric polynomial | 0ZNXZB4HNB | concept | 05E05 |
| Bipartite graph | 0ZVQKTRKVQ | concept | 05C75 |
