Displaying similar documents to “Light Graphs In Planar Graphs Of Large Girth”

Characterizations of planar plick graphs

V.R. Kulli, B. Basavanagoud (2004)

Discussiones Mathematicae Graph Theory

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In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar.

Note on enumeration of labeled split graphs

Vladislav Bína, Jiří Přibil (2015)

Commentationes Mathematicae Universitatis Carolinae

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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

2-distance 4-colorability of planar subcubic graphs with girth at least 22

Oleg V. Borodin, Anna O. Ivanova (2012)

Discussiones Mathematicae Graph Theory

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The trivial lower bound for the 2-distance chromatic number χ₂(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ₂ = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ₂(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.

Characterizing Cartesian fixers and multipliers

Stephen Benecke, Christina M. Mynhardt (2012)

Discussiones Mathematicae Graph Theory

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Let G ☐ H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24(3) (2004), 389-402] characterized prism fixers, i.e., graphs G for which γ(G ☐ K₂) = γ(G), and noted that γ(G ☐ Kₙ) ≥ min{|V(G)|, γ(G)+n-2}. We call a graph G a consistent fixer if γ(G ☐ Kₙ) = γ(G)+n-2 for each n such that 2 ≤ n < |V(G)|- γ(G)+2, and characterize this class of graphs. Also...

The Thickness of Amalgamations and Cartesian Product of Graphs

Yan Yang, Yichao Chen (2017)

Discussiones Mathematicae Graph Theory

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The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study...