2011/12/09 by Andrew Buchanan, Tanya Khovanova, Buchanan, Andrew +3
Computer Science · Engineering · Mathematics · #05B45 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05B45 #msc:05C69 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1112.2115
15 pages, 12 figures
arxiv created 2011/12/09 · openalex publication_date 2011/12/09 · arxiv updated 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A domino covering of a board is saturated if no domino is redundant. We introduce the concept of a fragment tiling and show that a minimal fragment tiling always corresponds to a maximal saturated domino covering. The size of a minimal fragment tiling is the domination number of the board. We define a class of regular boards and show that for these boards the domination number gives the size of a minimal X-pentomino covering. Natural sequences that count maximal saturated domino coverings of square and rectangular boards are obtained. These include the new sequences A193764, A193765, A193766, A193767, and A193768 of OEIS.