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  • In 1975, Erdős proposed the problem of determining the maximal number of edges in a graph on n vertices that contains no triangles or squares. In this paper we consider a generalized version of the problem, i.e., what is the maximum size of a graph of order n and girth at least t+1 (containing no cycles of length less than t + 1). We consider the problem on special types of graphs, such as pseudotrees, cacti, graphs lying in a square grid, Halin, generalized Halin and planar graphs. We give the extremal cases, some constructions and we use these results to obtain general lower bounds for the problem in the general case.
  • In 1975, Erdős proposed the problem of determining the maximal number of edges in a graph on n vertices that contains no triangles or squares. In this paper we consider a generalized version of the problem, i.e., what is the maximum size of a graph of order n and girth at least t+1 (containing no cycles of length less than t + 1). We consider the problem on special types of graphs, such as pseudotrees, cacti, graphs lying in a square grid, Halin, generalized Halin and planar graphs. We give the extremal cases, some constructions and we use these results to obtain general lower bounds for the problem in the general case. (en)
Title
  • Maximizing the size of planar graphs under girth constraints
  • Maximizing the size of planar graphs under girth constraints (en)
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  • Maximizing the size of planar graphs under girth constraints
  • Maximizing the size of planar graphs under girth constraints (en)
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  • RIV/49777513:23520/14:43924758!RIV15-MSM-23520___
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  • 27708
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  • RIV/49777513:23520/14:43924758
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  • girth; planar graph; extremal graph (en)
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  • CA - Kanada
http://linked.open...ontrolniKodProRIV
  • [78DAF5B68A0F]
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  • Journal of Combinatorial Mathematics and Combinatorial Computing
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  • 89
http://linked.open...iv/tvurceVysledku
  • Christou, Michalis
  • Iliopoulos, Costas
  • Millerová, Miroslava
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  • 0835-3026
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http://localhost/t...ganizacniJednotka
  • 23520
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