Skip to main content
added 14 characters in body; edited title
Source Link
Licheng Zhang
  • 1.9k
  • 6
  • 17

Is there any study on the bounds on the number of even cycles offor planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a problem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on the number of 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

Is there any study on the bounds on even cycles of planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a problem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

Is there any study on the bounds on the number of even cycles for planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a problem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on the number of 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

deleted 1 character in body
Source Link
Licheng Zhang
  • 1.9k
  • 6
  • 17

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a probelemproblem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a probelem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a problem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

edited body
Source Link
Licheng Zhang
  • 1.9k
  • 6
  • 17

Is there any study inon the bounds on even cycles of planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum Numbernumber of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a probelem about whether there is a similar result for planar bipartite graphs. For example, an upper boundupper bound on 4 cycles 4 cycles (or any other even cycleseven cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

Is there any study in the bounds on even cycles of planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum Number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a probelem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

Is there any study on the bounds on even cycles of planar bipartite graphs?

In 1979, Hakimi and Schmeichel [1] initiated such a study by determining the maximum number of triangles and 4-cycles possible in an $n$-vertex planar graph (see also [2] for a small correction).

  • [1] S. Hakimi, E. Schmeichel. On the Number of Cycles of Length k in a Maximal Planar Graph. J. Graph Theory 3 (1979): 69–86.

  • [2] A. Alameddine. On the Number of Cycles of Length 4 in a Maximal Planar Graph. J. GraphTheory, 4(1980): 417–422.

In 2019, Győri et al. [3] studied the maximum number of pentagons on planar graphs.

  • [3] Győri E, Paulos A, Salia N, et al. The maximum number of pentagons in a planar graph[J]. arXiv preprint arXiv:1909.13532, 2019.

I have a probelem about whether there is a similar result for planar bipartite graphs. For example, an upper bound on 4 cycles (or any other even cycles). I haven't found it yet. If not, it is not clear what the difficulty is.

I once asked a similar question at Math. Stack and did not seem to see any results.

edited body
Source Link
Licheng Zhang
  • 1.9k
  • 6
  • 17
Loading
Source Link
Licheng Zhang
  • 1.9k
  • 6
  • 17
Loading