Results 71 to 80 of about 17,567 (164)

On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords

Discussiones Mathematicae Graph Theory, 2019
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-planar graph with maximum degree ∆ ≥ 8 is edge-colorable with ∆ colors if each of its 5-cycles contains ...
Sun Lin, Wu Jianliang
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Large matchings in maximal 1-planar graphs

Discrete Mathematics
It is well-known that every maximal planar graph has a matching of size at least $\tfrac{n+8}{3}$ if $n\geq 14$. In this paper, we investigate similar matching-bounds for maximal \emph{1-planar} graphs, i.e., graphs that can be drawn such that every edge has at most one crossing.
Therese Biedl, John Wittnebel
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Strictly-convex drawings of 3-connected planar graphs

Journal of Computational Geometry
Strictly-convex straight-line drawings of $3$-connected planar graphs in small area form a classical research topic in Graph Drawing. Currently, the best-known area bound for such drawings of $n$-vertex graphs is $O(n^2) \times O(n^2)$, as shown by ...
Michael Bekos, Martin Gronemann, Fabrizio Montecchiani, Antonios Symvonis   +3 more
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On the k-Structure Ratio in Planar and Outerplanar Graphs

Discrete Mathematics & Theoretical Computer Science, 2008
A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-
Gruia Calinescu, Cristina G. Fernandes
doaj  

The maximum number of edges of bipartite 1-planar graphs with 1-disk drawings

AKCE International Journal of Graphs and Combinatorics
A graph is 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let G be a bipartite 1-planar graph with bipartition sets X and Y. A 1-disk [Formula: see text] drawing of G is a 1-planar drawing such that all vertices
Guiping Wang
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On the d-independence number in 1-planar graphs

Graphs and Combinatorics
The $d$-independence number of a graph $G$ is the largest possible size of an independent set $I$ in $G$ where each vertex of $I$ has degree at least $d$ in $G$. Upper bounds for the $d$-independence number in planar graphs are well-known for $d=3,4,5$, and can in fact be matched with constructions that actually have minimum degree $d$.
Therese Biedl, Prosenjit Bose, Babak Miraftab   +2 more
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On the Independence Number of 1-Planar Graphs.

An independent set in a graph is a set of vertices where no two vertices are adjacent to each other. A maximum independent set is the largest possible independent set that can be formed within a given graph G. The cardinality of this set is referred to as the independence number of G.
Biedl, Therese, Bose, Prosenjit, Miraftab, Babak   +2 more
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Straight-line drawings of 1-planar graphs

Computational Geometry
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges, so that edges of the same color do not cross.
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On randomly colouring locally sparse graphs

Discrete Mathematics & Theoretical Computer Science, 2006
We consider the problem of generating a random q-colouring of a graph G=(V,E). We consider the simple Glauber Dynamics chain. We show that if for all v ∈ V the average degree of the subgraph H v induced by the neighbours of v ∈ V is ≪Δ where Δ ...
Alan Frieze, Juan Vera
doaj  

Image contraction through fuzzy soft outerplanar graph structures. [PDF]

Sci Rep
Jaisankar D, Ramalingam S, Zegeye GB.
europepmc   +1 more source