Results 31 to 40 of about 543,681 (314)
On the edge irregularity strength for some classes of plane graphs
AIMS Mathematics, 2021 Graph labeling is an assignment of (usually) positive integers to elements of a graph (vertices and/or edges) satisfying certain condition(s). In the last two decades, graph labeling research received much attention from researchers.
Ibrahim Tarawneh +3 more
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Coloring distance graphs on the plane
Discrete Mathematics, 2023 We consider the coloring of certain distance graphs on the Euclidean plane. Namely, we ask for the minimal number of colors needed to color all points of the plane in such a way that pairs of points at distance in the interval $[1,b]$ get different colors. The classic Hadwiger-Nelson problem is a special case of this question -- obtained by taking $b=1$
Joanna Chybowska-Sokół +2 more
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A Survey on the Cyclic Coloring and its Relaxations
Discussiones Mathematicae Graph Theory, 2021 A cyclic coloring of a plane graph is a vertex coloring such that any two vertices incident with the same face receive distinct colors. This type of coloring was introduced more than fifty years ago, and a lot of research in chromatic graph theory was ...
Czap Július +2 more
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Drawings of Planar Graphs with Few Slopes and Segments [PDF]
, 2005 We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees.
Barát +29 more
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Invariants of Graph Drawings in the Plane [PDF]
Arnold Mathematical Journal, 2020 48 pages, many figures.
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A plane graph representation of triconnected graphs
Theoretical Computer Science, 2010 AbstractGiven a graph G=(V,E), a set S={s1,s2,…,sk} of k vertices of V, and k natural numbers n1,n2,…,nk such that ∑i=1kni=|V|, the k-partition problem is to find a partition V1,V2,…,Vk of the vertex set V such that |Vi|=ni, si∈Vi, and Vi induces a connected subgraph of G for each i=1,2,…,k. For the tripartition problem on a triconnected graph, a naive
Hiroshi Nagamochi +2 more
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Ars Mathematica Contemporanea, 2015 A plane graph is called alternating if all adjacent vertices have different degrees, and all neighboring faces as well. Alternating plane graphs were introduced in 2008. This paper presents the previous research on alternating plane graphs. There are two smallest alternating plane graphs, having 17 vertices and 17 faces each.
Althöfer, Ingo +4 more
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On Uniquely 3-Colorable Plane Graphs without Adjacent Faces of Prescribed Degrees
Mathematics, 2019 A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to the permutation of the colors. For a plane graph G, two faces f 1 and f 2 of G are adjacent ( i , j )-faces if d ( f 1 ) = i,
Zepeng Li +4 more
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On Visibility Representations of Non-planar Graphs [PDF]
, 2015 A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its endpoints. Testing
Biedl, Therese +2 more
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Facial graceful coloring of plane graphs [PDF]
Opuscula MathematicaLet \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors ...
Július Czap
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