Knowledge (XXG)

User:David Eppstein/Matroid Theory

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55: 117: 581: 336: 460: 54: 477: 495: 483: 313: 518: 565: 152: 454: 383: 187: 140: 128: 395: 365: 146: 448: 430: 377: 371: 193: 170: 134: 17: 243: 547: 471: 424: 412: 307: 278: 181: 553: 506: 489: 418: 359: 353: 324: 290: 202: 111: 541: 512: 213: 164: 105: 389: 301: 284: 158: 575: 442: 406: 219: 267: 255: 225: 88: 82: 559: 535: 237: 231: 436: 261: 99: 330: 529: 342: 249: 76: 25: 228: – Fewest graph edges whose removal breaks all cycles 445: – Matroid obtained by restrictions and contractions 91: – Maximum size of an independent set of the matroid 252: – Abstraction of disjoint paths in directed graphs 108: – Matroid in which every permutation is a symmetry 421: – Independence system partitionable into circuits 316: – Formulation of matroids using closure operators 198:
Pages displaying short descriptions of redirect targets
167: – Matroid that can be represented over all fields 216: – Matroid with graph forests as independent sets 463: – Characterization of planar graphs by matroids 137: – Vectors whose linear combinations are nonzero 79: – Abstraction of linear independence of vectors 190: – Set without nontrivial polynomial equalities 368: – Least-weight tree connecting graph vertices 339: – Realization of semialgebraic sets by points 222: – Tree which includes all vertices of a graph 120: – Geometric structure of 8 points and 8 lines 544: – Group-theoretic generalization of matroids 451: – Conjecture on forbidden minors of matroids 386: – Largest independent set of paired elements 240: – Cycles in a graph that generate all cycles 131: – Vectors with given pattern of independence 556: – Convex hull of indicator vectors of bases 427: – Partition of graph into sequence of paths 258: – Graph with a list of distinguished cycles 155: – Extension of independent vectors to bases 149: – Dimension of the column space of a matrix 143: – Set of vectors used to define coordinates 568: – Set-to-real map with diminishing returns 538: – Mathematical system of orderings or sets 515: – Abstract structure with colored elements 509: – Algebraic encoding of graph connectivity 362: – Objective function for greedy algorithms 161: – Abstraction of mod-2 vector independence 474: – Abstract geometry without 2-point lines 333: – Ternary relation on points in the plane 293: – Abstraction of bar-and-joint frameworks 532: – Set system used in greedy optimization 521: – Property of rank functions of matroids 492: – Points separated from others by a line 480: – Existence of a line through two points 433: – Hierarchical clustering of graph edges 374: – Shared independent set of two matroids 486: – On rearrangement of bases in matroids 380: – Subdivision into few independent sets 327: – Abstraction of ordered linear algebra 196: – Field extension that is not algebraic 184: – Abstraction of algebraic independence 114: – Matroid with no linear representation 8: 468:Matroid generalizations of discrete geometry 409: – Abstraction of graph shortest cycles 398: – Method for mathematical optimization 304: – Non-obvious mathematical equivalance 234: – All even-degree subgraphs of a graph 173: – Fewest dependent columns in a matrix 85: – Matroid with complemented basis sets 498: – Partition of space by a hyperplanes 457: – On composition of paths in matroids 439: – Gluing graphs at complete subgraphs 392: – Subroutine for testing independence 356: – Sequence of locally optimal choices 345: – Relation on disjoint pairs of sets 310: – Join-meet algebra on matroid flats 246: – Abstraction of unicyclic subgraphs 102: – Geometry with 7 points and 7 lines 415: – Abstraction of 2-colorable graphs 403:Matroid generalizations of graph theory 205: – Matroid associated with a group 550: – Set system related to matroids 287: – Matroid without short circuits 281: – Direct sum of uniform matroids 264: – Graph with group-labeled edges 562: – Multiset analogue of matroids 270: – Graph with sign-labeled edges 7: 275:Additional constructions of matroids 24: 298:Structures equivalent to matroids 350:Algorithmic problems on matroids 53: 178:Matroids from abstract algebra 1: 461:Whitney's planarity criterion 125:Matroids from linear algebra 337:Mnëv's universality theorem 598: 496:Arrangement of hyperplanes 314:Pregeometry (model theory) 582:User namespace book pages 52: 478:Sylvester–Gallai theorem 566:Submodular set function 484:Rota's basis conjecture 153:Steinitz exchange lemma 455:Tutte homotopy theorem 384:Matroid parity problem 188:Algebraic independence 141:Basis (linear algebra) 129:Matroid representation 519:Ingleton's inequality 396:Criss-cross algorithm 366:Minimum spanning tree 147:Rank (linear algebra) 431:Branch-decomposition 378:Matroid partitioning 372:Matroid intersection 210:Matroids from graphs 194:Transcendence degree 503:Matroid polynomials 171:Spark (mathematics) 135:Linear independence 18:User:David Eppstein 526:Related structures 244:Bicircular matroid 548:Matroid embedding 472:Sylvester matroid 449:Rota's conjecture 425:Ear decomposition 413:Bipartite matroid 321:Oriented matroids 308:Geometric lattice 279:Partition matroid 182:Algebraic matroid 65: 64: 61: 60: 44: 589: 554:Matroid polytope 507:Tutte polynomial 490:K-set (geometry) 419:Eulerian matroid 360:Weighted matroid 354:Greedy algorithm 325:Oriented matroid 291:Rigidity matroid 203:Dowling geometry 199: 57: 37: 30: 29: 26: 597: 596: 592: 591: 590: 588: 587: 586: 572: 571: 542:Coxeter matroid 513:Colored matroid 214:Graphic matroid 197: 165:Regular matroid 118:MacLane matroid 106:Uniform matroid 70: 41: 22: 21: 20: 12: 11: 5: 595: 593: 585: 584: 574: 573: 570: 569: 563: 557: 551: 545: 539: 533: 527: 523: 522: 516: 510: 504: 500: 499: 493: 487: 481: 475: 469: 465: 464: 458: 452: 446: 440: 434: 428: 422: 416: 410: 404: 400: 399: 393: 390:Matroid oracle 387: 381: 375: 369: 363: 357: 351: 347: 346: 340: 334: 328: 322: 318: 317: 311: 305: 302:Cryptomorphism 299: 295: 294: 288: 285:Paving matroid 282: 276: 272: 271: 265: 259: 253: 247: 241: 235: 229: 223: 217: 211: 207: 206: 200: 191: 185: 179: 175: 174: 168: 162: 159:Binary matroid 156: 150: 144: 138: 132: 126: 122: 121: 115: 109: 103: 97: 93: 92: 86: 80: 74: 73:Basic concepts 69: 68:Matroid Theory 66: 63: 62: 59: 58: 50: 49: 46: 45: 39:Matroid Theory 34: 33: 23: 15: 14: 13: 10: 9: 6: 4: 3: 2: 594: 583: 580: 579: 577: 567: 564: 561: 558: 555: 552: 549: 546: 543: 540: 537: 534: 531: 528: 525: 524: 520: 517: 514: 511: 508: 505: 502: 501: 497: 494: 491: 488: 485: 482: 479: 476: 473: 470: 467: 466: 462: 459: 456: 453: 450: 447: 444: 443:Matroid minor 441: 438: 435: 432: 429: 426: 423: 420: 417: 414: 411: 408: 407:Matroid girth 405: 402: 401: 397: 394: 391: 388: 385: 382: 379: 376: 373: 370: 367: 364: 361: 358: 355: 352: 349: 348: 344: 341: 338: 335: 332: 329: 326: 323: 320: 319: 315: 312: 309: 306: 303: 300: 297: 296: 292: 289: 286: 283: 280: 277: 274: 273: 269: 266: 263: 260: 257: 254: 251: 248: 245: 242: 239: 236: 233: 230: 227: 224: 221: 220:Spanning tree 218: 215: 212: 209: 208: 204: 201: 195: 192: 189: 186: 183: 180: 177: 176: 172: 169: 166: 163: 160: 157: 154: 151: 148: 145: 142: 139: 136: 133: 130: 127: 124: 123: 119: 116: 113: 112:Vámos matroid 110: 107: 104: 101: 98: 95: 94: 90: 87: 84: 81: 78: 75: 72: 71: 67: 56: 51: 48: 47: 43: 40: 36: 35: 32: 31: 28: 27: 19: 268:Signed graph 256:Biased graph 226:Circuit rank 89:Matroid rank 83:Dual matroid 42: 38: 560:Polymatroid 536:Antimatroid 238:Cycle basis 232:Cycle space 437:Clique-sum 262:Gain graph 100:Fano plane 331:CC system 576:Category 530:Greedoid 343:Separoid 96:Examples 250:Gammoid 77:Matroid 16:< 578::

Index

User:David Eppstein
Matroid Theory

Matroid
Dual matroid
Matroid rank
Fano plane
Uniform matroid
Vámos matroid
MacLane matroid
Matroid representation
Linear independence
Basis (linear algebra)
Rank (linear algebra)
Steinitz exchange lemma
Binary matroid
Regular matroid
Spark (mathematics)
Algebraic matroid
Algebraic independence
Transcendence degree
Dowling geometry
Graphic matroid
Spanning tree
Circuit rank
Cycle space
Cycle basis
Bicircular matroid
Gammoid
Biased graph

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