Intersection Dimension and Maximum Degree

Aravind, N. R.; Subramanian, C. R.

doi:10.1016/j.endm.2009.11.058

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Strong Coloring and Circular-arc Graphs1

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2018

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(2 citation statements)

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“…We also thank Sebastian Siebertz for his remark on graphs excluding a subdivision of K t , and N.R. Aravind for calling references [2], [7], and [22] to our attention. The presentation of the paper was significantly improved thanks to the comments and suggestions of two anonymous reviewers.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Since there are 2 Θ(∆n log n) n-vertex graphs of maximum degree ∆, it follows that almost all graphs of maximum degree ∆ have circular dimension Ω(∆). On the other hand, it was proved by Aravind and Subramanian [2] that every graph of maximum degree ∆ has circular dimension O(∆ log ∆/ log log ∆).…”

Section: Strong Coloring and Circular-arc Graphsmentioning

confidence: 99%

See 1 more Smart Citation

Boxicity, Poset Dimension, and Excluded Minors

Wiechert

2018

Electron. J. Combin.

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In this short note, we relate the boxicity of graphs (and the dimension of posets) with their generalized coloring parameters. In particular, together with known estimates, our results imply that any graph with no $K_t$-minor can be represented as the intersection of $O(t^2\log t)$ interval graphs (improving the previous bound of $O(t^4)$), and as the intersection of $\tfrac{15}2 t^2$ circular-arc graphs.

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Section: Acknowledgementsmentioning

confidence: 99%

Section: Strong Coloring and Circular-arc Graphsmentioning

confidence: 99%