Results 31 to 40 of about 3,901 (159)
A Note on Edge‐Group Choosability of Planar Graphs without 5‐Cycles
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 This paper is devoted to a study of the concept of edge‐group choosability of graphs. We say that G is edge‐k‐group choosable if its line graph is k‐group choosable. In this paper, we study an edge‐group choosability version of Vizing conjecture for planar graphs without 5‐cycles and for planar graphs without noninduced 5‐cycles (2010 Mathematics ...
Amir Khamseh, Andrei V. Kelarev
wiley +1 more source
A note on zero-divisor graph of amalgamated duplication of a ring along an ideal
AKCE International Journal of Graphs and Combinatorics, 2017 Let be a commutative ring and be a non-zero ideal of . Let be the subring of consisting of the elements for and . In this paper we characterize all isomorphism classes of finite commutative rings with identity and ideal such that is planar.
A. Mallika, R. Kala
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Directed Acyclic Outerplanar Graphs Have Constant Stack Number [PDF]
TheoretiCSThe stack number of a directed acyclic graph $G$ is the minimum $k$ for which there is a topological ordering of $G$ and a $k$-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ...
Paul Jungeblut +2 more
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Nonplanarity of Iterated Line Graphs
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 The 1‐crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G has crossing number greater than 1. In this paper, we show that the 1‐crossing index of a graph is either infinite or it is at most 5. Moreover, we give a full characterization of all graphs with respect to their 1‐crossing index.
Jing Wang, Alfred Peris
wiley +1 more source
Pathwidth of outerplanar graphs [PDF]
Journal of Graph Theory, 2006 We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin, after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant $c ...
Coudert, David +2 more
openaire +5 more sources
The Planar Index and Outerplanar Index of Some Graphs Associated to Commutative Rings
Discussiones Mathematicae - General Algebra and Applications, 2019 In this paper, we study the planar and outerplanar indices of some graphs associated to a commutative ring. We give a full characterization of these graphs with respect to their planar and outerplanar indices when R is a finite ring.
Barati Zahra, Afkhami Mojgan
doaj +1 more source
, 2004 A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two monochromatic edges ...
Dujmovic, Vida +2 more
core +5 more sources
Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs
Journal of Applied Mathematics, Volume 2020, Issue 1, 2020., 2020 Let G = (V, E) be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph G a proper coloring where no two adjacent vertices are signed with the same color. Alice′s goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by χg(G), while Bob′s goal is
Ramy Shaheen +3 more
wiley +1 more source
Algorithms, 2013 The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry.
Takeyuki Tamura, Tatsuya Akutsu
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, 2018 Has appeared in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)
Steven Chaplick +4 more
openaire +4 more sources