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Existence of certain skew room frames with application to weakly 3‐chromatic linear spaces
Author(s) -
Rodger C. A.,
Wantland E. B.,
Chen K.,
Zhu L.
Publication year - 1994
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180020505
Subject(s) - mathematics , skew , chromatic scale , combinatorics , integer (computer science) , space (punctuation) , discrete mathematics , telecommunications , computer science , programming language , operating system
It is shown that for any even integer n ≥ 16 and for some b ≥ 1, there exists a skew Room frame of type 2 a 4 b with n = 2 a + 4 b . As an application, we show that for any integer v ≡ 1,4 (mod 12), there exists a weakly 3‐chromatic linear space with all lines having size 4 iff v > 16. This answers an open problem posed by Colbourn and Rosa. © 1994 John Wiley & Sons, Inc.