Results 91 to 100 of about 3,724 (174)
Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs
Discussiones Mathematicae Graph Theory, 2015 Given graphs G and H, a vertex coloring c : V (G) →ℕ is an H-free coloring of G if no color class contains a subgraph isomorphic to H. The H-free chromatic number of G, χ (H,G), is the minimum number of colors in an H-free coloring of G.
Kubicka Ewa +2 more
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Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth
, 2014 We investigate crossing minimization for 1-page and 2-page book drawings. We show that computing the 1-page crossing number is fixed-parameter tractable with respect to the number of crossings, that testing 2-page planarity is fixed-parameter tractable ...
Bannister, Michael J., Eppstein, David
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Planar linear arrangements of outerplanar graphs
IEEE Transactions on Circuits and Systems, 1988 Given an n-vertex outerplanar graph G, we consider the problem of arranging the vertices of G on a line such that no two edges cross and various cost measures are minimized. We present efficient algorithms for generating layouts in which every edge (i,j) of G does not exceed a given bandwidth b(i,j), the total edge length and the cutwidth of the layout
Frederickson, Greg N. +1 more
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DEFICIENCY OF OUTERPLANAR GRAPHS
Proceedings of the YSU A: Physical and Mathematical Sciences, 2017 An edge-coloring of a graph G with colors $1,2,...,t$ is an interval $t$-coloring, if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval $t$-coloring for some positive integer $t$.
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To Prove Four Color Theorem [PDF]
, 2016 In this paper, we give a proof for four color theorem(four color conjecture). Our proof does not involve computer assistance and the most important is that it can be generalized to prove Hadwiger Conjecture. Moreover, we give algorithms to color and test
Cao, Weiwei, Yue, Weiya
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Injective Chromatic Number of Outerplanar Graphs
Taiwanese Journal of Mathematics, 2018 An injective coloring of a graph is a vertex coloring where two vertices with common neighbor receive distinct colors. The minimum integer $k$ that $G$ has a $k-$injective coloring is called injective chromatic number of $G$ and denoted by $ _i(G)$. In this paper, the injective chromatic number of outerplanar graphs with maximum degree $ $ and girth $
Mozafari-Nia, Mahsa, Omoomi, Behnaz
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A Note on the Fair Domination Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2020 For k ≥ 1, a k-fair dominating set (or just kFD-set), in a graph G is a dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V − S. The k-fair domination number of G, denoted by fdk(G), is the minimum cardinality of a kFD-set. A fair dominating
Hajian Majid, Rad Nader Jafari
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Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs [PDF]
Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices,
Laskar, R.C., Mulder, H.M., Novick, B.
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Characterizations of outerplanar graphs
Discrete Mathematics, 1979 AbstractThe paper presents several characterizations of outerplanar graphs, some of them are counterparts of the well-known characterizations of planar graphs and the other provide very efficient tools for outerplanarity testing, coding (i.e. isomorphism testing), and counting such graphs.
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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
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