Necessary conditions for the existence of two classes of ZCPS-Wh(vv)

Let vv denote an integer, v≡0,1(mod4) and set X=Zm∪AX=Zm∪A where m=v−1m=v−1, A={∞}A={∞} when v≡0(mod4), m=vm=v, A=0̸A=0̸ when v≡1(mod4). A ZZ-cyclic Wh(v)(v) is said to be a ZZ-cyclic patterned starter   whist tournament on vv players, ZCPSZCPS-Wh(v)(v), when the initial round partner pairs form the patterned starter for the set XX. In this study, we develop necessary conditions for the existence of ZCPSZCPS-Wh(v)(v) for the cases v=3Qv=3Q, QQ an integer of the form 4h+34h+3 and v=3R+1v=3R+1, RR an integer of the form 4h+14h+1.