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EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE

Year 2015, Volume: 3 Issue: 1, 121 - 125, 01.04.2015

Abstract

Let S = (P;L) be a non-trivial regular nite linear space with v points, v + k lines, k  3: We show that if S contains at least 􀀀k 2  lines of size b(p) 􀀀 2 and one line size b(p) for some point p, then S is embeddable in a unique projective plane  of order b(p) 􀀀 1 and  􀀀 s is a complete graph of order k ; where b(p)  4 for some point p:

References

  • [1] Batten , L.M. and Beutelspacher, A. ; Combinatorics of points and lines, Cambridge Univer- sity Press, 1993.
  • [2] Batten, L.M. ; Embedding pseudo-complements in nite projective planes, Ars Combin. 24 (1987), 129-132.
  • [3] Bose , R.C. and Shrikhande, S.S. ; Embedding the complement of a oval in a projective plane of even order, Discrete Math. 6 (1973), 305-312.
  • [4] Bruck, R. H. ; Existence problems for classes of nite projective planes, Lectures delivered to the Canadian Math. Congress, Sask., Aug.1963.
  • [5] De Brujin N.G and Erdos, P. ; On a combinatorial problem, Nederl Akad.Wetemsch. proc. Sect. Sci. 51 (1948), 1277 - 1279.
  • [6] De Witte, P. ;The exceptional case in a Theorem of Bose and Shrikhande, J. Austral.Math. soc. 24 (Series A) (1977), 64-78.
  • [7] Dickey, L. J. ; Embedding the complement of a unital in a projective plane, Atti del convegno di Geometria Combinatoria e sue Applicazioni, Perugia, 1971, pp. 199-203.
  • [8] Gunaltl, _I. and Olgun, S. ; On the embedding some linear spaces in nite projective planes. J.geom. 68 (2000) 96-99.
  • [9] Gunaltl, _I. , Anapa, P. and Olgun, S. ; On the embedding of complements of some hyperbolic planes. Ars Combin. 80 (2006), pp. 205-214.
  • [10] Hall, M. ; Projective planes, Trans. Amer. Math. Soc. 54 (1943) 229-277.
  • [11] Kaya, R. and  Ozcan, E. ; On the construction of B-L planes from projective planes, Rendiconti del Seminario Matematico Di Bresciot (1984), pp. 427-434.
  • [12] Mullin, R.C. and Vanstone, S.A. ; Embedding the pseudo-complements of a quadrilateral in a nite projective plane, Ann.New York Acad.Sci.319, 405-412.
  • [13] Totten, J. ; Embedding the complement of two lines in a nite projective plane, J.Austral.Math.Soc. 22 (Series A) (1976), 27-34.
Year 2015, Volume: 3 Issue: 1, 121 - 125, 01.04.2015

Abstract

References

  • [1] Batten , L.M. and Beutelspacher, A. ; Combinatorics of points and lines, Cambridge Univer- sity Press, 1993.
  • [2] Batten, L.M. ; Embedding pseudo-complements in nite projective planes, Ars Combin. 24 (1987), 129-132.
  • [3] Bose , R.C. and Shrikhande, S.S. ; Embedding the complement of a oval in a projective plane of even order, Discrete Math. 6 (1973), 305-312.
  • [4] Bruck, R. H. ; Existence problems for classes of nite projective planes, Lectures delivered to the Canadian Math. Congress, Sask., Aug.1963.
  • [5] De Brujin N.G and Erdos, P. ; On a combinatorial problem, Nederl Akad.Wetemsch. proc. Sect. Sci. 51 (1948), 1277 - 1279.
  • [6] De Witte, P. ;The exceptional case in a Theorem of Bose and Shrikhande, J. Austral.Math. soc. 24 (Series A) (1977), 64-78.
  • [7] Dickey, L. J. ; Embedding the complement of a unital in a projective plane, Atti del convegno di Geometria Combinatoria e sue Applicazioni, Perugia, 1971, pp. 199-203.
  • [8] Gunaltl, _I. and Olgun, S. ; On the embedding some linear spaces in nite projective planes. J.geom. 68 (2000) 96-99.
  • [9] Gunaltl, _I. , Anapa, P. and Olgun, S. ; On the embedding of complements of some hyperbolic planes. Ars Combin. 80 (2006), pp. 205-214.
  • [10] Hall, M. ; Projective planes, Trans. Amer. Math. Soc. 54 (1943) 229-277.
  • [11] Kaya, R. and  Ozcan, E. ; On the construction of B-L planes from projective planes, Rendiconti del Seminario Matematico Di Bresciot (1984), pp. 427-434.
  • [12] Mullin, R.C. and Vanstone, S.A. ; Embedding the pseudo-complements of a quadrilateral in a nite projective plane, Ann.New York Acad.Sci.319, 405-412.
  • [13] Totten, J. ; Embedding the complement of two lines in a nite projective plane, J.Austral.Math.Soc. 22 (Series A) (1976), 27-34.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İbrahim Günaltı

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Günaltı, İ. (2015). EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp Journal of Mathematics, 3(1), 121-125.
AMA Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. April 2015;3(1):121-125.
Chicago Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 121-25.
EndNote Günaltı İ (April 1, 2015) EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp Journal of Mathematics 3 1 121–125.
IEEE İ. Günaltı, “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”, Konuralp J. Math., vol. 3, no. 1, pp. 121–125, 2015.
ISNAD Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics 3/1 (April 2015), 121-125.
JAMA Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. 2015;3:121–125.
MLA Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 121-5.
Vancouver Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. 2015;3(1):121-5.
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