Appendix to
On the Shannon Capacity of Triangular Graphs
Ashik Mathew Kizhakkepallathu, Patric RJ Östergård, Alexandru Popa
Electronic Journal of Combinatorics 20(2):P27 (2013).


A packing attaining H(3,7) = 35:

(6,1) (5,2) (5,4), (6,1) (6,3) (6,4), (6,3) (6,5) (3,2), 
(6,3) (4,1) (2,1), (3,0) (4,3) (6,3), (4,2) (6,5) (5,3), 
(1,0) (5,0) (3,2), (5,4) (4,2) (2,1), (5,3) (6,2) (5,4), 
(2,1) (4,1) (6,4), (4,2) (4,3) (5,0), (6,4) (2,1) (3,0), 
(5,3) (5,1) (5,0), (4,2) (3,0) (3,2), (5,1) (6,1) (3,2), 
(4,2) (6,5) (2,0), (5,3) (4,3) (5,4), (1,0) (5,4) (1,0), 
(5,3) (2,0) (3,0), (2,0) (2,1) (5,1), (1,0) (4,3) (5,2), 
(6,3) (5,2) (6,1), (6,5) (4,3) (3,0), (6,4) (4,0) (6,4), 
(4,0) (6,1) (6,4), (5,3) (1,0) (6,4), (4,0) (5,2) (6,4), 
(6,0) (6,0) (5,0), (5,2) (6,5) (6,1), (4,1) (1,0) (5,1), 
(6,5) (3,0) (2,1), (2,0) (2,1) (3,2), (2,0) (3,0) (4,1), 
(2,1) (2,0) (6,0), (3,1) (6,3) (1,0).

A packing attaining H(3,13) >= 248:

(12, 10) (1, 0) (1, 0), (11, 10) (3, 2) (1, 0),
(11, 9) (5, 4) (1, 0), (9, 0) (12, 6) (1, 0),
(1, 0) (8, 1) (1, 0), (11, 10) (10, 0) (6, 5),
(11, 9) (10, 9) (2, 1), (12, 2) (11, 7) (4, 1),
(3, 2) (5, 4) (1, 0), (4, 3) (12, 6) (1, 0),
(5, 4) (9, 8) (1, 0), (6, 5) (11, 10) (12, 10),
(5, 4) (7, 0) (1, 0), (6, 5) (2, 1) (1, 0),
(7, 6) (4, 3) (1, 0), (8, 7) (6, 5) (1, 0),
(12, 8) (12, 8) (1, 0), (12, 10) (10, 9) (1, 0),
(11, 10) (11, 7) (1, 0), (11, 9) (1, 0) (2, 1),
(9, 0) (3, 2) (2, 1), (1, 0) (5, 4) (2, 1),
(2, 1) (12, 6) (2, 1), (3, 2) (9, 8) (2, 1),
(4, 3) (11, 10) (1, 0), (3, 2) (1, 0) (2, 1),
(4, 3) (3, 2) (2, 1), (5, 4) (5, 4) (2, 1),
(6, 5) (12, 6) (2, 1), (7, 6) (9, 0) (4, 1),
(7, 5) (11, 10) (8, 1), (11, 10) (9, 0) (8, 7),
(8, 7) (2, 1) (2, 1), (12, 8) (4, 3) (2, 1),
(12, 10) (6, 5) (2, 1), (11, 10) (12, 8) (2, 1),
(11, 9) (10, 9) (12, 0), (1, 0) (10, 5) (12, 0),
(1, 0) (1, 0) (3, 2), (2, 1) (3, 2) (3, 2),
(3, 2) (5, 4) (3, 2), (4, 3) (12, 6) (3, 2),
(5, 4) (1, 0) (3, 2), (3, 2) (12, 6) (9, 6),
(5, 4) (9, 8) (3, 2), (6, 5) (3, 2) (3, 2),
(7, 6) (5, 4) (3, 2), (8, 7) (12, 6) (3, 2),
(12, 8) (9, 8) (3, 2), (8, 7) (10, 9) (10, 0),
(12, 8) (7, 0) (9, 8), (12, 10) (2, 1) (3, 2),
(11, 10) (4, 3) (3, 2), (11, 9) (6, 5) (3, 2),
(9, 0) (12, 8) (3, 2), (1, 0) (10, 9) (3, 2),
(8, 7) (10, 4) (12, 11), (3, 2) (1, 0) (4, 3),
(4, 3) (3, 2) (4, 3), (5, 4) (5, 4) (4, 3),
(7, 6) (9, 0) (3, 2), (6, 0) (11, 10) (11, 4),
(1, 0) (10, 9) (10, 1), (7, 6) (8, 1) (4, 3),
(8, 7) (3, 2) (4, 3), (12, 8) (5, 4) (4, 3),
(12, 10) (12, 6) (4, 3), (11, 10) (9, 8) (4, 3),
(12, 7) (11, 10) (3, 2), (11, 10) (7, 0) (4, 3),
(11, 9) (2, 1) (4, 3), (9, 0) (4, 3) (4, 3),
(1, 0) (6, 5) (4, 3), (2, 1) (12, 8) (4, 3),
(3, 2) (10, 9) (4, 3), (4, 3) (11, 7) (11, 3),
(5, 4) (1, 0) (5, 4), (6, 5) (3, 2) (5, 4),
(7, 6) (5, 4) (5, 4), (8, 7) (12, 6) (5, 4),
(12, 8) (9, 8) (5, 4), (12, 10) (3, 2) (5, 4),
(11, 4) (7, 0) (12, 9), (12, 8) (12, 6) (10, 9),
(11, 10) (5, 4) (5, 4), (11, 9) (12, 6) (5, 4),
(9, 0) (9, 8) (7, 4), (9, 1) (11, 10) (5, 4),
(9, 0) (7, 0) (5, 4), (1, 0) (2, 1) (5, 4),
(2, 1) (4, 3) (5, 4), (3, 2) (6, 5) (5, 4),
(4, 3) (12, 8) (5, 4), (5, 4) (10, 9) (5, 4),
(7, 5) (11, 7) (5, 4), (7, 6) (1, 0) (6, 5),
(8, 7) (3, 2) (6, 5), (12, 8) (5, 4) (6, 5),
(12, 10) (12, 6) (6, 5), (11, 10) (9, 1) (6, 5),
(11, 9) (3, 2) (6, 5), (11, 0) (11, 7) (8, 2),
(8, 1) (7, 0) (4, 1), (9, 0) (8, 5) (6, 5),
(1, 0) (12, 6) (6, 5), (2, 1) (9, 8) (6, 5),
(3, 2) (11, 10) (6, 5), (2, 1) (7, 0) (11, 5),
(3, 2) (2, 1) (6, 5), (4, 3) (4, 3) (6, 5),
(5, 4) (6, 5) (6, 5), (6, 5) (12, 8) (6, 5),
(7, 6) (10, 9) (6, 5), (1, 0) (11, 7) (12, 3),
(12, 8) (1, 0) (7, 6) , (12, 10) (3, 2) (7, 6),
(11, 10) (5, 4) (7, 6), (9, 0) (9, 4) (6, 5),
(9, 0) (11, 7) (9, 6), (12, 7) (11, 7) (7, 6),
(6, 5) (12, 6) (4, 3), (1, 0) (3, 2) (7, 6),
(2, 1) (5, 4) (7, 6), (3, 2) (12, 6) (8, 7),
(4, 3) (9, 8) (7, 6), (6, 1) (11, 10) (8, 7),
(4, 3) (7, 0) (7, 6), (5, 4) (2, 1) (7, 6),
(6, 5) (4, 3) (7, 6), (7, 6) (6, 5) (7, 6),
(8, 7) (12, 8) (7, 6), (12, 8) (10, 9) (7, 6),
(10, 8) (11, 7) (7, 6), (2, 1) (1, 0) (10, 7),
(11, 9) (3, 2) (8, 7), (9, 0) (5, 4) (8, 7),
(1, 0) (12, 6) (8, 7), (2, 1) (8, 7) (8, 7),
(4, 3) (11, 10) (12, 7), (11, 6) (11, 7) (6, 5),
(3, 2) (3, 2) (8, 7), (4, 3) (5, 4) (8, 7),
(5, 4) (12, 6) (8, 7), (6, 5) (9, 8) (8, 7),
(12, 2) (11, 10) (10, 8), (6, 5) (7, 0) (8, 7),
(7, 6) (2, 1) (8, 7), (8, 7) (4, 3) (8, 7),
(12, 8) (6, 5) (8, 7), (12, 10) (12, 8) (8, 7),
(11, 10) (10, 1) (8, 7), (9, 0) (11, 7) (7, 1),
(9, 0) (1, 0) (9, 8), (1, 0) (3, 2) (9, 8),
(2, 1) (4, 1) (9, 8), (7, 6) (8, 7) (2, 1),
(4, 3) (8, 1) (9, 8), (9, 2) (11, 7) (3, 2),
(3, 0) (10, 9) (9, 8), (5, 4) (3, 2) (9, 8),
(6, 5) (5, 4) (9, 8), (7, 6) (12, 6) (9, 8),
(8, 7) (9, 8) (9, 8), (11, 9) (12, 6) (7, 6),
(8, 7) (7, 1) (11, 10), (12, 8) (2, 1) (9, 8),
(12, 10) (4, 3) (9, 8), (11, 10) (6, 5) (9, 8),
(11, 9) (12, 8) (9, 8), (9, 4) (10, 9) (9, 8),
(4, 3) (11, 7) (10, 4), (2, 1) (9, 5) (9, 8),
(3, 2) (3, 2) (10, 9), (4, 3) (5, 4) (10, 9),
(5, 4) (12, 6) (10, 9), (8, 6) (11, 10) (9, 3),
(10, 4) (11, 7) (8, 5), (6, 5) (1, 0) (10, 9),
(1, 0) (11, 7) (10, 0), (8, 7) (5, 4) (10, 9),
(7, 6) (3, 2) (10, 9), (12, 10) (9, 8) (10, 9),
(10, 9) (11, 10) (11, 10), (12, 10) (7, 0) (10, 2),
(11, 10) (2, 1) (10, 9), (11, 9) (4, 3) (10, 9),
(9, 0) (6, 5) (10, 9), (1, 0) (12, 8) (10, 9),
(5, 1) (11, 10) (11, 9), (6, 5) (9, 8) (10, 9),
(4, 3) (1, 0) (11, 10), (5, 4) (3, 2) (11, 10),
(6, 5) (5, 4) (11, 10), (7, 6) (12, 6) (11, 10),
(8, 7) (8, 0) (11, 10), (11, 10) (11, 10) (4, 3),
(3, 2) (7, 0) (12, 0), (12, 8) (3, 2) (11, 10),
(12, 10) (5, 4) (11, 10), (11, 10) (12, 6) (11, 10),
(11, 9) (8, 7) (11, 10), (5, 2) (11, 10) (7, 0),
(11, 9) (9, 0) (11, 10), (9, 0) (2, 1) (11, 10),
(1, 0) (4, 3) (11, 10), (2, 1) (6, 5) (11, 10),
(3, 2) (12, 8) (11, 10), (4, 3) (10, 9) (11, 10),
(8, 6) (11, 10) (2, 1), (12, 5) (1, 0) (12, 11),
(7, 6) (3, 2) (12, 11), (8, 7) (9, 5) (12, 11),
(12, 8) (12, 6) (12, 11), (12, 10) (9, 8) (12, 11),
(5, 4) (11, 10) (6, 2), (10, 6) (1, 0) (12, 11),
(11, 10) (3, 2) (12, 11), (11, 9) (5, 4) (12, 11),
(9, 0) (12, 6) (12, 11), (1, 0) (9, 8) (12, 11),
(10, 2) (11, 10) (12, 9), (12, 8) (7, 0) (5, 3),
(2, 1) (2, 1) (12, 11), (3, 2) (4, 3) (12, 11),
(4, 3) (6, 5) (12, 11), (5, 4) (12, 8) (12, 11),
(6, 5) (9, 7) (12, 11), (12, 8) (10, 1) (5, 4),
(8, 7) (1, 0) (12, 0), (12, 8) (3, 2) (12, 0),
(12, 10) (5, 4) (12, 0), (11, 10) (12, 6) (12, 0),
(11, 9) (8, 1) (12, 0), (12, 7) (11, 7) (12, 0),
(2, 1) (7, 0) (9, 6), (9, 0) (3, 2) (12, 0),
(1, 0) (4, 0) (12, 0), (2, 1) (12, 6) (12, 0),
(3, 2) (9, 8) (12, 0), (12, 11) (11, 10) (11, 9),
(2, 1) (3, 2) (1, 0), (4, 3) (2, 1) (12, 0),
(5, 4) (4, 3) (12, 0), (6, 5) (6, 5) (12, 0),
(7, 6) (12, 8) (12, 0), (9, 0) (1, 0) (7, 6),
(9, 8) (11, 7) (12, 0), (7, 3) (7, 0) (9, 8).

Two non-isomorphic packings attaining H(3,5)=12

(4, 0) (3, 0) (1, 0), 
(3, 1) (4, 0) (2, 0), 
(2, 0) (4, 1) (2, 0), 
(4, 3) (2, 1) (2, 1), 
(4, 1) (2, 1) (3, 0), 
(2, 0) (4, 2) (3, 1), 
(3, 1) (4, 3) (3, 1), 
(4, 2) (3, 0) (3, 2), 
(3, 2) (3, 2) (4, 0), 
(2, 1) (1, 0) (4, 1), 
(1, 0) (3, 2) (4, 2), 
(3, 0) (1, 0) (4, 3);


(3, 1) (4, 0) (1, 0), 
(2, 0) (4, 1) (1, 0), 
(4, 3) (2, 1) (2, 1), 
(4, 0) (3, 0) (2, 1), 
(4, 1) (2, 1) (3, 0), 
(4, 2) (3, 0) (3, 0), 
(2, 0) (4, 2) (3, 2), 
(3, 1) (4, 3) (3, 2), 
(3, 0) (3, 2) (4, 0), 
(2, 1) (3, 2) (4, 1), 
(2, 1) (1, 0) (4, 2), 
(3, 0) (1, 0) (4, 3).

A packing attaining H(4,5)=27:

(4, 0) (4, 0) (3, 0) (1, 0),
(2, 0) (2, 0) (4, 1) (2, 0),
(2, 0) (2, 0) (4, 2) (3, 1),
(1, 0) (1, 0) (3, 2) (4, 2),
(3, 0) (3, 0) (1, 0) (4, 3),
(3, 1) (1, 0) (4, 0) (2, 0),
(4, 3) (3, 0) (2, 1) (2, 1),
(4, 1) (1, 0) (2, 1) (3, 0),
(3, 1) (1, 0) (4, 3) (3, 1),
(4, 2) (2, 0) (3, 0) (3, 2),
(3, 2) (2, 0) (3, 2) (4, 0),
(2, 1) (1, 0) (1, 0) (4, 1),
(4, 0) (3, 1) (4, 0) (2, 0),
(1, 0) (4, 3) (2, 1) (2, 1),
(2, 0) (4, 1) (2, 1) (3, 0),
(4, 0) (3, 1) (4, 3) (3, 1),
(3, 0) (4, 2) (3, 0) (3, 2),
(4, 0) (3, 2) (3, 2) (4, 0),
(4, 0) (2, 1) (1, 0) (4, 1),
(2, 1) (4, 3) (4, 0) (2, 0),
(4, 3) (4, 2) (4, 1) (2, 0),
(4, 3) (4, 2) (4, 2) (3, 1),
(2, 1) (4, 3) (4, 3) (3, 1),
(3, 1) (4, 3) (3, 2) (4, 0),
(3, 2) (4, 2) (1, 0) (4, 1),
(4, 2) (4, 1) (3, 2) (4, 2),
(4, 1) (4, 3) (1, 0) (4, 3).