Knowledge (XXG)

List edge-coloring

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47:. An instance of a list edge-coloring problem consists of a graph together with a list of allowed colors for each edge. A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color. 348: 316: 371: 288: 240: 236: 387: 344: 175: 367: 325: 114: 17: 36: 381: 218: 44: 40: 311: 28: 201:), i.e. the list chromatic index and the chromatic index agree asymptotically ( 358:
Kahn, Jeff (2000), "Asymptotics of the list chromatic index for multigraphs",
339:
Jensen, Tommy R.; Toft, Bjarne (1995), "12.20 List-Edge-Chromatic Numbers",
330: 251:
The most famous open problem about list edge-coloring is probably the
372:
10.1002/1098-2418(200009)17:2<117::AID-RSA3>3.0.CO;2-9
314:(1995), "The list chromatic index of a bipartite multigraph", 287:, is the special case of the list coloring conjecture for the 113:-edge-choosable. It is conjectured that it always equals the 283:
overview its history. The Dinitz conjecture, proven by
65:as its underlying graph and that provides at least 343:, New York: Wiley-Interscience, pp. 201–202, 61:if every instance of list edge-coloring that has 8: 280: 329: 284: 179: 7: 279:This conjecture has a fuzzy origin; 202: 360:Random Structures & Algorithms 25: 69:allowed colors for each edge of 317:Journal of Combinatorial Theory 1: 73:has a proper coloring. The 404: 83:list edge chromatic number 289:complete bipartite graphs 281:Jensen & Toft (1995) 253:list coloring conjecture 247:List coloring conjecture 237:complete bipartite graph 18:List coloring conjecture 341:Graph Coloring Problems 331:10.1006/jctb.1995.1011 79:list edge colorability 125:Some properties of ch 101:is the least number 87:list chromatic index 193:) < (1 + o(1))χ 33:list edge-coloring 176:Dinitz conjecture 75:edge choosability 16:(Redirected from 395: 374: 353: 334: 333: 270: 262: 212: 196: 188: 159: 148: 140: 128: 92: 21: 403: 402: 398: 397: 396: 394: 393: 392: 378: 377: 357: 351: 338: 310: 307: 300: 268: 260: 249: 234: 219:chromatic index 210: 194: 186: 174:. This is the 169: 157: 146: 138: 126: 123: 115:chromatic index 90: 59:-edge-choosable 23: 22: 15: 12: 11: 5: 401: 399: 391: 390: 388:Graph coloring 380: 379: 376: 375: 366:(2): 117–156, 355: 349: 336: 306: 303: 292: 277: 276: 248: 245: 226: 207: 206: 183: 161: 154: 122: 119: 39:that combines 37:graph coloring 24: 14: 13: 10: 9: 6: 4: 3: 2: 400: 389: 386: 385: 383: 373: 369: 365: 361: 356: 352: 350:0-471-02865-7 346: 342: 337: 332: 327: 323: 319: 318: 313: 309: 308: 304: 302: 299: 295: 290: 286: 285:Galvin (1995) 282: 274: 266: 258: 257: 256: 254: 246: 244: 242: 238: 233: 229: 224: 220: 216: 204: 200: 192: 184: 181: 180:Galvin (1995) 177: 173: 168: 164: 155: 152: 144: 136: 135: 134: 132: 120: 118: 116: 112: 108: 104: 100: 96: 88: 84: 80: 76: 72: 68: 64: 60: 58: 53: 48: 46: 45:edge coloring 42: 41:list coloring 38: 35:is a type of 34: 30: 19: 363: 359: 340: 321: 320:, Series B, 315: 312:Galvin, Fred 297: 293: 278: 272: 264: 252: 250: 241:partite sets 231: 227: 222: 214: 208: 198: 190: 178:, proven by 171: 166: 162: 150: 142: 130: 124: 110: 106: 102: 98: 94: 86: 82: 78: 74: 70: 66: 62: 56: 55: 51: 49: 32: 26: 324:: 153–158, 239:with equal 97:) of graph 29:mathematics 305:References 145:) < 2 χ 121:Properties 105:such that 217:) is the 203:Kahn 2000 382:Category 50:A graph 225:; and K 347:  235:, the 209:Here χ 267:) = χ 85:, or 77:, or 345:ISBN 170:) = 89:, ch 43:and 368:doi 326:doi 221:of 133:): 109:is 54:is 27:In 384:: 364:17 362:, 322:63 301:. 275:). 259:ch 255:. 243:. 205:). 185:ch 160:(K 156:ch 153:). 137:ch 117:. 81:, 31:, 370:: 354:. 335:. 328:: 298:n 296:, 294:n 291:K 273:G 271:( 269:′ 265:G 263:( 261:′ 232:n 230:, 228:n 223:G 215:G 213:( 211:′ 199:G 197:( 195:′ 191:G 189:( 187:′ 182:. 172:n 167:n 165:, 163:n 158:′ 151:G 149:( 147:′ 143:G 141:( 139:′ 131:G 129:( 127:′ 111:k 107:G 103:k 99:G 95:G 93:( 91:′ 71:G 67:k 63:G 57:k 52:G 20:)

Index

List coloring conjecture
mathematics
graph coloring
list coloring
edge coloring
chromatic index
Dinitz conjecture
Galvin (1995)
Kahn 2000
chromatic index
complete bipartite graph
partite sets
Jensen & Toft (1995)
Galvin (1995)
complete bipartite graphs
Galvin, Fred
Journal of Combinatorial Theory
doi
10.1006/jctb.1995.1011
ISBN
0-471-02865-7
doi
10.1002/1098-2418(200009)17:2<117::AID-RSA3>3.0.CO;2-9
Category
Graph coloring

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