Oriented diameter of maximal outerplanar graphs

Wang, Xiaolin; Chen, Yaojun; Dankelmann, Peter; Guo, Yubao; Surmacs, Michel; Volkmann, Lutz

doi:10.1002/jgt.22707

Cited by 7 publications

(1 citation statement)

References 10 publications

(12 reference statements)

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“…The paper by Chvátal and Thomassen [5] has led to further investigation of such bounds on the oriented diameter given certain graph parameters, including the diameter [10,15,19], the radius [4], the domination number [11,20], the maximum degree [8], the minimum degree [2,7,26], the number of edges of the graph [6], and other graph classes [3,12,13,14,15,17,18,21,22,23,24,27,28].…”

Section: Definitionsmentioning

confidence: 99%

Large Girth and Small Oriented Diameter Graphs

Cochran¹

2022

Preprint

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In 2015, Dankelmann and Bau proved that for every bridgeless graph G of order n and minimum degree δ there is an orientation of diameter at most 11 n δ+1 + 9. In 2016, Surmacs reduced this bound to 7 n δ+1 . In this paper, we consider the girth of a graph g and show that for any ε > 0 there is a bound of the form (2g + ε) n h(δ,g) + O(1), where h(δ, g) is a polynomial. Letting g = 3 and ε < 1 gives an inprovement on the result by Surmacs.

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Section: Definitionsmentioning

confidence: 99%

Large Girth and Small Oriented Diameter Graphs

Cochran¹

2022

Preprint

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Bounds for the Oriented Diameter of Planar Triangulations

Mondal

Parthiban²,

Indra³

2022

Frontiers of Algorithmic Wisdom

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The Oriented Diameter of Graphs with Given Connected Domination Number and Distance Domination Number

Dankelmann,

Morgan,

Rivett-Carnac

2024

Graphs and Combinatorics

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Let G be a bridgeless graph. An orientation of G is a digraph obtained from G by assigning a direction to each edge. The oriented diameter of G is the minimum diameter among all strong orientations of G. The connected domination number $$\gamma _c(G)$$ γ c ( G ) of G is the minimum cardinality of a set S of vertices of G such that every vertex of G is in S or adjacent to some vertex of S, and which induces a connected subgraph in G. We prove that the oriented diameter of a bridgeless graph G is at most $$2 \gamma _c(G) +3$$ 2 γ c ( G ) + 3 if $$\gamma _c(G)$$ γ c ( G ) is even and $$2 \gamma _c(G) +2$$ 2 γ c ( G ) + 2 if $$\gamma _c(G)$$ γ c ( G ) is odd. This bound is sharp. For $$d \in {\mathbb {N}}$$ d ∈ N , the d-distance domination number $$\gamma ^d(G)$$ γ d ( G ) of G is the minimum cardinality of a set S of vertices of G such that every vertex of G is at distance at most d from some vertex of S. As an application of a generalisation of the above result on the connected domination number, we prove an upper bound on the oriented diameter of the form $$(2d+1)(d+1)\gamma ^d(G)+ O(d)$$ ( 2 d + 1 ) ( d + 1 ) γ d ( G ) + O ( d ) . Furthermore, we construct bridgeless graphs whose oriented diameter is at least $$(d+1)^2 \gamma ^d(G) +O(d)$$ ( d + 1 ) 2 γ d ( G ) + O ( d ) , thus demonstrating that our above bound is best possible apart from a factor of about 2.

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Oriented diameter of maximal outerplanar graphs

Cited by 7 publications

References 10 publications

Large Girth and Small Oriented Diameter Graphs

Large Girth and Small Oriented Diameter Graphs

Bounds for the Oriented Diameter of Planar Triangulations

The Oriented Diameter of Graphs with Given Connected Domination Number and Distance Domination Number

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