Clique number for hypergraphs

Question

Does anybody know any link/source where I can find examples of hypergraphs with their clique numbers? I need a few examples to test an algorithm and do not want to go for randomly generated hypergraph. Any help will be appreciated.

Answer 1

Interpretion: set bits and dark dots are nodes present in the clique. The number is just the binary in base 10, and the digit in parens is the color.

H: A complete 3-uniform hypergraph on 10 vertices with 2 colors, cliques: 27, edges: 120

Maximal Color-Cliques
  color 0:
    order 2:
      ▪⬝⬝▪⬝⬝⬝⬝⬝⬝ 1001000000 (576) (0)
      ⬝⬝⬝⬝⬝▪▪⬝⬝⬝ 0000011000 (24) (0)
    order 4:
      ▪▪⬝⬝▪⬝⬝▪⬝⬝ 1100100100 (804) (0)
      ⬝▪⬝▪▪⬝⬝▪⬝⬝ 0101100100 (356) (0)
      ⬝▪▪⬝▪⬝▪⬝⬝⬝ 0110101000 (424) (0)
      ⬝▪▪⬝▪▪⬝⬝⬝⬝ 0110110000 (432) (0)
    order 5:
      ⬝⬝⬝⬝▪⬝▪▪▪▪ 0000101111 (47) (0)
      ⬝⬝⬝⬝▪▪⬝▪▪▪ 0000110111 (55) (0)
      ⬝▪⬝▪⬝⬝▪⬝▪▪ 0101001011 (331) (0)
      ⬝▪⬝▪⬝▪⬝⬝▪▪ 0101010011 (339) (0)
      ⬝⬝▪▪▪⬝⬝⬝▪▪ 0011100011 (227) (0)
      ⬝▪▪⬝⬝⬝⬝▪▪▪ 0110000111 (391) (0)
      ▪⬝▪⬝▪⬝⬝⬝▪▪ 1010100011 (675) (0)
      ▪▪⬝⬝⬝⬝▪⬝▪▪ 1100001011 (779) (0)
      ▪▪⬝⬝⬝▪⬝⬝▪▪ 1100010011 (787) (0)
  color 1:
    order 2:
      ⬝⬝⬝⬝⬝⬝⬝⬝▪▪ 0000000011 (3) (1)
    order 3:
      ⬝▪⬝⬝▪⬝⬝⬝▪⬝ 0100100010 (290) (1)
      ⬝▪⬝⬝▪⬝⬝⬝⬝▪ 0100100001 (289) (1)
      ⬝⬝▪⬝▪⬝⬝▪⬝⬝ 0010100100 (164) (1)
    order 4:
      ▪▪▪▪⬝⬝⬝⬝⬝⬝ 1111000000 (960) (1)
      ⬝⬝▪⬝⬝▪▪⬝⬝▪ 0010011001 (153) (1)
      ⬝⬝▪⬝⬝▪▪⬝▪⬝ 0010011010 (154) (1)
      ⬝▪⬝⬝⬝▪▪▪⬝⬝ 0100011100 (284) (1)
      ▪⬝⬝▪⬝⬝⬝▪⬝▪ 1001000101 (581) (1)
      ▪⬝⬝▪⬝⬝⬝▪▪⬝ 1001000110 (582) (1)
    order 5:
      ▪⬝⬝▪▪▪▪⬝⬝⬝ 1001111000 (632) (1)
    order 6:
      ▪⬝▪▪⬝▪▪▪⬝⬝ 1011011100 (732) (1)

H: A complete 3-uniform hypergraph on 8 vertices with 3 colors, cliques: 30, edges: 56

Maximal Color-Cliques
  color 0:
    order 2:
      ⬝▪⬝⬝⬝⬝⬝▪ 01000001 (65) (0)
      ⬝⬝▪⬝⬝▪⬝⬝ 00100100 (36) (0)
    order 3:
      ▪▪▪⬝⬝⬝⬝⬝ 11100000 (224) (0)
      ▪⬝⬝▪⬝▪⬝⬝ 10010100 (148) (0)
      ⬝▪⬝▪⬝⬝▪⬝ 01010010 (82) (0)
      ⬝▪⬝⬝▪▪⬝⬝ 01001100 (76) (0)
      ⬝⬝▪▪▪⬝⬝⬝ 00111000 (56) (0)
    order 4:
      ▪⬝▪⬝⬝⬝▪▪ 10100011 (163) (0)
      ▪⬝⬝▪▪⬝⬝▪ 10011001 (153) (0)
      ⬝⬝⬝⬝▪▪▪▪ 00001111 (15) (0)
  color 1:
    order 2:
      ⬝⬝▪⬝⬝▪⬝⬝ 00100100 (36) (1)
    order 3:
      ⬝⬝⬝▪⬝⬝▪▪ 00010011 (19) (1)
      ⬝⬝⬝▪▪▪⬝⬝ 00011100 (28) (1)
      ⬝⬝▪⬝▪⬝⬝▪ 00101001 (41) (1)
      ▪▪⬝⬝⬝⬝⬝▪ 11000001 (193) (1)
      ▪⬝▪▪⬝⬝⬝⬝ 10110000 (176) (1)
      ▪⬝⬝⬝⬝▪⬝▪ 10000101 (133) (1)
      ⬝▪⬝▪▪⬝⬝⬝ 01011000 (88) (1)
    order 4:
      ▪▪⬝⬝▪⬝▪⬝ 11001010 (202) (1)
      ▪▪⬝⬝⬝▪▪⬝ 11000110 (198) (1)
      ⬝▪▪⬝▪⬝▪⬝ 01101010 (106) (1)
  color 2:
    order 2:
      ▪⬝⬝⬝⬝⬝⬝▪ 10000001 (129) (2)
    order 3:
      ▪▪⬝▪⬝⬝⬝⬝ 11010000 (208) (2)
      ▪⬝⬝▪⬝⬝▪⬝ 10010010 (146) (2)
      ⬝⬝⬝▪▪⬝▪⬝ 00011010 (26) (2)
      ⬝▪⬝⬝▪⬝⬝▪ 01001001 (73) (2)
      ⬝▪⬝⬝⬝⬝▪▪ 01000011 (67) (2)
    order 4:
      ⬝⬝▪▪⬝▪▪⬝ 00110110 (54) (2)
      ▪⬝▪⬝▪▪⬝⬝ 10101100 (172) (2)
    order 5:
      ⬝▪▪▪⬝▪⬝▪ 01110101 (117) (2)

H: A complete 3-uniform hypergraph on 8 vertices with 4 colors, cliques: 42, edges: 56

Maximal Color-Cliques
  color 0:
    order 2:
      ⬝⬝⬝▪▪⬝⬝⬝ 00011000 (24) (0)
    order 3:
      ▪▪⬝⬝▪⬝⬝⬝ 11001000 (200) (0)
      ⬝⬝▪⬝▪⬝⬝▪ 00101001 (41) (0)
      ⬝⬝▪⬝▪⬝▪⬝ 00101010 (42) (0)
      ⬝⬝▪⬝▪▪⬝⬝ 00101100 (44) (0)
      ▪⬝▪▪⬝⬝⬝⬝ 10110000 (176) (0)
      ▪⬝⬝⬝⬝▪▪⬝ 10000110 (134) (0)
      ▪⬝⬝⬝⬝▪⬝▪ 10000101 (133) (0)
      ⬝▪⬝▪⬝▪⬝⬝ 01010100 (84) (0)
      ⬝▪▪⬝⬝⬝⬝▪ 01100001 (97) (0)
    order 4:
      ⬝▪⬝▪⬝⬝▪▪ 01010011 (83) (0)
  color 1:
    order 3:
      ⬝⬝⬝⬝▪⬝▪▪ 00001011 (11) (1)
      ▪▪⬝⬝⬝⬝▪⬝ 11000010 (194) (1)
      ▪⬝⬝▪⬝⬝⬝▪ 10010001 (145) (1)
      ▪⬝⬝⬝▪▪⬝⬝ 10001100 (140) (1)
      ⬝▪▪⬝▪⬝⬝⬝ 01101000 (104) (1)
      ⬝▪⬝▪▪⬝⬝⬝ 01011000 (88) (1)
      ⬝▪⬝⬝⬝▪⬝▪ 01000101 (69) (1)
    order 4:
      ▪⬝▪⬝⬝⬝▪▪ 10100011 (163) (1)
      ⬝⬝▪▪⬝▪▪⬝ 00110110 (54) (1)
  color 2:
    order 2:
      ⬝⬝⬝▪⬝▪⬝⬝ 00010100 (20) (2)
      ⬝⬝⬝⬝▪▪⬝⬝ 00001100 (12) (2)
    order 3:
      ⬝⬝⬝⬝⬝▪▪▪ 00000111 (7) (2)
      ▪▪⬝▪⬝⬝⬝⬝ 11010000 (208) (2)
      ⬝⬝▪▪⬝⬝⬝▪ 00110001 (49) (2)
      ⬝⬝▪▪▪⬝⬝⬝ 00111000 (56) (2)
      ⬝▪⬝⬝▪⬝⬝▪ 01001001 (73) (2)
      ⬝▪▪⬝⬝⬝▪⬝ 01100010 (98) (2)
      ▪⬝⬝⬝▪⬝⬝▪ 10001001 (137) (2)
    order 4:
      ▪▪▪⬝⬝▪⬝⬝ 11100100 (228) (2)
      ▪⬝⬝▪▪⬝▪⬝ 10011010 (154) (2)
  color 3:
    order 2:
      ⬝⬝⬝⬝⬝⬝▪▪ 00000011 (3) (3)
      ▪⬝⬝⬝⬝⬝▪⬝ 10000010 (130) (3)
      ⬝⬝▪⬝⬝⬝▪⬝ 00100010 (34) (3)
      ⬝⬝⬝▪⬝⬝▪⬝ 00010010 (18) (3)
    order 3:
      ▪▪⬝⬝⬝⬝⬝▪ 11000001 (193) (3)
      ▪⬝▪⬝▪⬝⬝⬝ 10101000 (168) (3)
      ▪⬝⬝▪⬝▪⬝⬝ 10010100 (148) (3)
      ⬝▪▪▪⬝⬝⬝⬝ 01110000 (112) (3)
      ⬝⬝▪⬝⬝▪⬝▪ 00100101 (37) (3)
    order 4:
      ⬝▪⬝⬝▪▪▪⬝ 01001110 (78) (3)
      ⬝⬝⬝▪▪▪⬝▪ 00011101 (29) (3)

H: A complete 4-uniform hypergraph on 8 vertices with 2 colors, cliques: 34, edges: 70

Maximal Color-Cliques
  color 0:
    order 3:
      ⬝⬝⬝▪▪⬝⬝▪ 00011001 (25) (0)
    order 4:
      ▪▪▪⬝⬝▪⬝⬝ 11100100 (228) (0)
      ⬝⬝⬝▪▪▪▪⬝ 00011110 (30) (0)
      ▪▪⬝▪▪⬝⬝⬝ 11011000 (216) (0)
      ⬝⬝▪⬝▪▪▪⬝ 00101110 (46) (0)
      ▪⬝▪▪▪⬝⬝⬝ 10111000 (184) (0)
      ⬝⬝▪▪⬝▪▪⬝ 00110110 (54) (0)
      ▪⬝⬝▪▪▪⬝⬝ 10011100 (156) (0)
    order 5:
      ▪▪▪⬝▪⬝▪⬝ 11101010 (234) (0)
      ▪▪▪⬝▪⬝⬝▪ 11101001 (233) (0)
      ▪▪⬝▪⬝▪▪⬝ 11010110 (214) (0)
      ▪▪⬝▪⬝▪⬝▪ 11010101 (213) (0)
      ⬝▪▪▪⬝⬝▪▪ 01110011 (115) (0)
      ▪⬝▪⬝⬝▪▪▪ 10100111 (167) (0)
      ⬝▪⬝⬝▪▪▪▪ 01001111 (79) (0)
  color 1:
    order 4:
      ⬝⬝⬝▪⬝▪▪▪ 00010111 (23) (1)
      ▪▪▪▪⬝⬝⬝⬝ 11110000 (240) (1)
      ▪▪⬝⬝▪▪⬝⬝ 11001100 (204) (1)
      ⬝⬝▪⬝▪⬝▪▪ 00101011 (43) (1)
      ▪▪⬝⬝⬝⬝▪▪ 11000011 (195) (1)
      ▪⬝▪▪⬝▪⬝⬝ 10110100 (180) (1)
      ▪⬝▪▪⬝⬝▪⬝ 10110010 (178) (1)
      ⬝⬝▪▪▪⬝▪⬝ 00111010 (58) (1)
      ▪⬝▪▪⬝⬝⬝▪ 10110001 (177) (1)
      ⬝▪⬝▪▪⬝⬝▪ 01011001 (89) (1)
      ⬝▪⬝▪▪⬝▪⬝ 01011010 (90) (1)
      ▪⬝▪⬝▪▪⬝⬝ 10101100 (172) (1)
      ⬝▪▪⬝⬝▪⬝▪ 01100101 (101) (1)
      ⬝▪▪⬝⬝▪▪⬝ 01100110 (102) (1)
      ▪⬝⬝⬝▪▪▪⬝ 10001110 (142) (1)
      ▪⬝⬝⬝▪▪⬝▪ 10001101 (141) (1)
    order 5:
      ⬝▪▪▪▪▪⬝⬝ 01111100 (124) (1)
      ⬝⬝▪▪▪▪⬝▪ 00111101 (61) (1)
      ▪⬝⬝▪▪⬝▪▪ 10011011 (155) (1)