Existence of certain skew room frames with application to weakly 3‐chromatic linear spaces | Zendy

Rodger C. A. | Zendy; Wantland E. B. | Zendy; Chen K. | Zendy; Zhu L. | Zendy

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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.

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