Knowledge

File:7-hole and antihole.svg

Source 📝

614:"}},"text\/plain":{"en":{"":"checksum"}}},"{\"value\":\"476dc26f6234491ce8841bdf2c1882b4962ec357\",\"type\":\"string\"}":{"text\/html":{"en":{"P4092":"476dc26f6234491ce8841bdf2c1882b4962ec357"}},"text\/plain":{"en":{"P4092":"476dc26f6234491ce8841bdf2c1882b4962ec357"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":459,\"id\":\"P459\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 494:"}},"text\/plain":{"en":{"":"inception"}}},"{\"value\":{\"time\":\"+2012-08-06T00:00:00Z\",\"timezone\":0,\"before\":0,\"after\":0,\"precision\":11,\"calendarmodel\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q1985727\"},\"type\":\"time\"}":{"text\/html":{"en":{"P571":"6 August 2012"}},"text\/plain":{"en":{"P571":"6 August 2012"}}}}": --> 295: 610: 90: 209: 315:"}},"text\/plain":{"en":{"P2093":"David Eppstein","P4174":"David Eppstein"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 307:"}},"text\/plain":{"en":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:David_Eppstein"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 576:"}},"text\/plain":{"en":{"":"media type"}}},"{\"value\":\"image\\\/svg+xml\",\"type\":\"string\"}":{"text\/html":{"en":{"P1163":"image\/svg+xml"}},"text\/plain":{"en":{"P1163":"image\/svg+xml"}}}}": --> 618:"}},"text\/plain":{"en":{"":"determination method"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":13414952,\"id\":\"Q13414952\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P459":" 406:"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":88088423,\"id\":\"Q88088423\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":" 532:"}},"text\/plain":{"en":{"":"source of file"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P7482":" 450:"}},"text\/plain":{"en":{"":"copyright license"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":6938433,\"id\":\"Q6938433\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":" 681:"}},"text\/plain":{"en":{"":"data size"}}},"{\"value\":{\"amount\":\"+4219\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q8799\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P3575":"4,219 726:"}},"text\/plain":{"en":{"":"height"}}},"{\"value\":{\"amount\":\"+235\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q355198\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P2048":"235 771:"}},"text\/plain":{"en":{"":"width"}}},"{\"value\":{\"amount\":\"+435\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q355198\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P2049":"435 299:"}},"text\/plain":{"en":{"":"creator"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2699,\"id\":\"P2699\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 767: 230:
by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
144:
A seven-vertex odd cycle and its complement, showing in both cases an optimal coloring of the graph and a maximum clique. Since neither of the graphs uses a number of colors equal to its clique size, they are not
312: 932: 957: 304: 619: 533: 407: 451: 768: 723: 678: 611: 573: 529: 403: 316: 308: 300: 615: 491: 447: 296: 410:"}},"text\/plain":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder"}}}}": --> 927: 952: 64: 60: 56: 52: 48: 42: 663: 559: 433: 477: 101: 73: 782: 737: 692: 629: 583: 543: 417: 381: 368: 353: 536:"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}": --> 388: 656: 501: 461: 326: 285: 454:"}},"text\/plain":{"en":{"P275":"Creative Commons CC0 License"}}}}": --> 942: 319:"}},"text\/plain":{"en":{"":"Wikimedia username"}}}}": --> 880:
The following pages on the English Knowledge use this file (pages on other projects are not listed):
685:"}},"text\/plain":{"en":{"P3575":"4,219 byte"}}}}": --> 360: 775:"}},"text\/plain":{"en":{"P2049":"435 pixel"}}}}": --> 730:"}},"text\/plain":{"en":{"P2048":"235 pixel"}}}}": --> 109: 622:"}},"text\/plain":{"en":{"P459":"SHA-1"}}}}": --> 889: 218: 215: 178: 967: 8: 864: 853: 848: 37: 227: 96: 275: 194:
I, the copyright holder of this work, hereby publish it under the following license:
146: 226:
The person who associated a work with this deed has dedicated the work to the
884: 792: 747: 702: 639: 593: 553: 511: 471: 427: 336: 821:
Click on a date/time to view the file as it appeared at that time.
434:
copyrighted, dedicated to the public domain by copyright holder
408:
copyrighted, dedicated to the public domain by copyright holder
907: 917: 305:
https:\/\/commons.wikimedia.org\/wiki\/user:David_Eppstein
158: 84: 234:
http://creativecommons.org/publicdomain/zero/1.0/deed.en
269:
Add a one-line explanation of what this file represents
78:(SVG file, nominally 435 × 235 pixels, file size: 4 KB) 878: 898: 819: 108:
Commons is a freely licensed media file repository.
361:https://commons.wikimedia.org/user:David_Eppstein 240:Creative Commons Zero, Public Domain Dedication 89: 154: 131: 174: 164: 14: 772: 727: 682: 41:Size of this PNG preview of this SVG file: 219:CC0 1.0 Universal Public Domain Dedication 900:The following other wikis use this file: 645:476dc26f6234491ce8841bdf2c1882b4962ec357 202: 214:This file is made available under the 120: 197: 812: 13: 274: 268: 193: 138: 121: 71: 981: 273: 879: 259: 207: 201: 88: 31: 21: 256: 208: 139: 895: 816: 255: 26: 1: 560:original creation by uploader 534:original creation by uploader 933:Теорема о совершенных графах 875: 478:Creative Commons CC0 License 452:Creative Commons CC0 License 281:Items portrayed in this file 187: 7: 958:Теорема про досконалі графи 10: 986: 964:Usage on zh.wikipedia.org 949:Usage on uk.wikipedia.org 939:Usage on sr.wikipedia.org 924:Usage on ru.wikipedia.org 914:Usage on it.wikipedia.org 904:Usage on de.wikipedia.org 128: 123: 813: 200: 168: 16: 258: 95:This is a file from the 36: 870: 157: 134:7-hole and antihole.svg 99:. Information from its 102:description page there 890:Perfect graph theorem 849:00:59, 7 August 2012 657:determination method 616:determination method 65:2,560 × 1,383 pixels 47:Other resolutions: 382:Wikimedia username 369:author name string 317:Wikimedia username 309:author name string 61:1,280 × 691 pixels 57:1,024 × 553 pixels 896:Global file usage 873: 774: 729: 684: 462:copyright license 448:copyright license 267: 252: 251: 184: 183: 117: 116: 97:Wikimedia Commons 32:Global file usage 977: 928:Совершенный граф 861: 823: 801: 756: 711: 666: 661: 418:copyright status 404:copyright status 391: 386: 376: 373: 363: 358: 265: 247: 244: 241: 238: 235: 216:Creative Commons 211: 210: 205: 204: 198: 170: 160: 143: 135: 129: 113: 92: 91: 85: 79: 68: 53:640 × 346 pixels 49:320 × 173 pixels 43:435 × 235 pixels 985: 984: 980: 979: 978: 976: 975: 974: 953:Досконалий граф 908:Perfekter Graph 894: 881: 874: 867: 859: 815: 814: 811: 810: 809: 808: 807: 806: 805: 804: 802: 799: 789: 788: 787: 785: 766: 765: 764: 763: 762: 761: 760: 759: 757: 754: 744: 743: 742: 740: 721: 720: 719: 718: 717: 716: 715: 714: 712: 709: 699: 698: 697: 695: 676: 675: 674: 673: 672: 671: 670: 669: 668: 667: 662: 659: 650: 649: 648: 646: 636: 635: 634: 632: 609: 608: 607: 606: 605: 604: 603: 602: 600: 590: 589: 588: 586: 571: 570: 569: 568: 567: 566: 565: 564: 562: 550: 549: 548: 546: 527: 526: 525: 524: 523: 522: 521: 520: 518: 508: 507: 506: 504: 489: 488: 487: 486: 485: 484: 483: 482: 480: 468: 467: 466: 464: 445: 444: 443: 442: 441: 440: 439: 438: 436: 424: 423: 422: 420: 401: 400: 399: 398: 397: 396: 395: 394: 393: 392: 387: 384: 378: 377: 374: 371: 365: 364: 359: 356: 347: 346: 345: 343: 333: 332: 331: 329: 294: 293: 292: 291: 290: 288: 272: 271: 270: 253: 245: 242: 239: 236: 233: 196: 195: 190: 185: 150: 133: 126: 119: 118: 107: 106: 105:is shown below. 81: 77: 70: 69: 46: 12: 11: 5: 983: 973: 972: 971: 970: 962: 961: 960: 955: 947: 946: 945: 937: 936: 935: 930: 922: 921: 920: 918:Grafo perfetto 912: 911: 910: 897: 893: 892: 887: 877: 872: 871: 869: 866:David Eppstein 865: 862: 856: 851: 846: 842: 841: 838: 835: 832: 829: 826: 818: 803: 797: 795: 794: 793: 791: 790: 786: 781: 779: 778: 777: 776: 770: 758: 752: 750: 749: 748: 746: 745: 741: 736: 734: 733: 732: 731: 725: 713: 707: 705: 704: 703: 701: 700: 696: 691: 689: 688: 687: 686: 680: 655: 654: 653: 652: 651: 647: 644: 642: 641: 640: 638: 637: 633: 628: 626: 625: 624: 623: 621: 617: 613: 601: 598: 596: 595: 594: 592: 591: 587: 582: 580: 579: 578: 577: 575: 563: 558: 556: 555: 554: 552: 551: 547: 544:source of file 542: 540: 539: 538: 537: 535: 531: 530:source of file 519: 516: 514: 513: 512: 510: 509: 505: 500: 498: 497: 496: 495: 493: 481: 476: 474: 473: 472: 470: 469: 465: 460: 458: 457: 456: 455: 453: 449: 437: 432: 430: 429: 428: 426: 425: 421: 416: 414: 413: 412: 411: 409: 405: 389:David Eppstein 380: 379: 375:David Eppstein 367: 366: 352: 351: 350: 349: 348: 344: 341: 339: 338: 337: 335: 334: 330: 325: 323: 322: 321: 320: 318: 314: 313:David Eppstein 310: 306: 302: 298: 289: 284: 282: 279: 278: 277: 276: 264: 263: 260: 257: 250: 249: 223: 222: 212: 192: 191: 189: 186: 182: 181: 179:David Eppstein 176: 172: 171: 166: 162: 161: 156: 152: 151: 147:perfect graphs 136: 127: 125: 122: 115: 114: 93: 83: 82: 40: 35: 34: 29: 24: 19: 9: 6: 4: 3: 2: 982: 969: 966: 965: 963: 959: 956: 954: 951: 950: 948: 944: 941: 940: 938: 934: 931: 929: 926: 925: 923: 919: 916: 915: 913: 909: 906: 905: 903: 902: 901: 891: 888: 886: 885:Perfect graph 883: 882: 868: 863: 857: 855: 852: 850: 847: 844: 843: 839: 836: 833: 830: 827: 825: 824: 822: 796: 784: 780: 751: 739: 735: 706: 694: 690: 665: 658: 643: 631: 627: 599:image/svg+xml 597: 585: 581: 561: 557: 545: 541: 517:6 August 2012 515: 503: 499: 479: 475: 463: 459: 435: 431: 419: 415: 390: 383: 370: 362: 355: 340: 328: 324: 287: 283: 280: 261: 254: 248: 229: 228:public domain 225: 224: 220: 217: 213: 199: 180: 177: 173: 167: 163: 159:6 August 2012 153: 148: 142: 137: 130: 111: 104: 103: 98: 94: 87: 86: 80: 75: 74:Original file 66: 62: 58: 54: 50: 44: 39: 33: 30: 28: 25: 23: 20: 18: 15: 943:Савршен граф 899: 820: 817:File history 232: 140: 110:You can help 100: 72: 22:File history 132:Description 876:File usage 858:435 × 235 834:Dimensions 584:media type 574:media type 342:some value 27:File usage 831:Thumbnail 828:Date/Time 693:data size 679:data size 502:inception 492:inception 188:Licensing 141:English: 630:checksum 612:checksum 262:Captions 169:Own work 845:current 840:Comment 327:creator 297:creator 286:depicts 266:English 124:Summary 76:‎ 860:(4 KB) 738:height 724:height 708:4,219 206:  175:Author 165:Source 968:完美图定理 800:pixel 783:width 773:pixel 769:width 755:pixel 728:pixel 664:SHA-1 620:SHA-1 246:false 243:false 837:User 798:435 753:235 710:byte 683:byte 155:Date 17:File 354:URL 301:URL 237:CC0 660:: 385:: 372:: 357:: 221:. 63:| 59:| 55:| 51:| 45:. 149:. 112:. 67:.

Index

File
File history
File usage
Global file usage
File:7-hole and antihole.svg
435 × 235 pixels
320 × 173 pixels
640 × 346 pixels
1,024 × 553 pixels
1,280 × 691 pixels
2,560 × 1,383 pixels
Original file
Wikimedia Commons
description page there
You can help
perfect graphs
David Eppstein
Creative Commons
CC0 1.0 Universal Public Domain Dedication
public domain
depicts
creator<\/a>"}},"text\/plain":{"en":{"":"creator"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2699,\"id\":\"P2699\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"URL<\/a>"}},"text\/plain":{"en":{"":"URL"}}},"{\"value\":\"https:\\\/\\\/commons.wikimedia.org\\\/wiki\\\/user:David_Eppstein\",\"type\":\"string\"}":{"text\/html":{"en":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:David_Eppstein<\/a>"}},"text\/plain":{"en":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:David_Eppstein"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"author name string<\/a>"}},"text\/plain":{"en":{"":"author name string"}}},"{\"value\":\"David Eppstein\",\"type\":\"string\"}":{"text\/html":{"en":{"P2093":"David Eppstein","P4174":"David Eppstein<\/a>"}},"text\/plain":{"en":{"P2093":"David Eppstein","P4174":"David Eppstein"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"Wikimedia username<\/a>"}},"text\/plain":{"en":{"":"Wikimedia username"}}}}">

creator
URL
https://commons.wikimedia.org/user:David_Eppstein
author name string
Wikimedia username
David Eppstein
copyright status<\/a>"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":88088423,\"id\":\"Q88088423\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder<\/a>"}},"text\/plain":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder"}}}}">