Results 41 to 50 of about 850,474 (224)
Star edge coloring of $ K_{2, t} $-free planar graphs
AIMS Mathematics, 2023 The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
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On the Planarity of Generalized Line Graphs
Theory and Applications of Graphs, 2019 One of the most familiar derived graphs is the line graph. The line graph $L(G)$ of a graph $G$ is that graph whose vertices are the edges of $G$ where two vertices of $L(G)$ are adjacent if the corresponding edges are adjacent in~$G$.
Khawlah H. Alhulwah +2 more
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On the Edge-Length Ratio of Outerplanar Graphs [PDF]
Theoretical Computer Science, 2018 We show that any outerplanar graph admits a planar straightline drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any $ > 0$ there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than $2 - $.
Lazard S., Lenhart W. J., Liotta G.
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On Supergraphs Satisfying CMSO Properties [PDF]
Logical Methods in Computer Science, 2021 Let CMSO denote the counting monadic second order logic of graphs. We give a constructive proof that for some computable function $f$, there is an algorithm $\mathfrak{A}$ that takes as input a CMSO sentence $\varphi$, a positive integer $t$, and a ...
Mateus de Oliveira Oliveira
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Adjacency posets of outerplanar graphs [PDF]
Discrete Mathematics, 2021 Felsner, Li and Trotter showed that the dimension of the adjacency poset of an outerplanar graph is at most 5, and gave an example of an outerplanar graph whose adjacency poset has dimension 4. We improve their upper bound to 4, which is then best possible.
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The Degree-Diameter Problem for Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2017 For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that nΔ,D=ΔD2+O (ΔD2−1)$n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2 ...
Dankelmann Peter +2 more
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On Another Class of Strongly Perfect Graphs
Mathematics, 2022 For a commutative ring R with unity, the associate ring graph, denoted by AG(R), is a simple graph with vertices as nonzero elements of R and two distinct vertices are adjacent if they are associates.
Neha Kansal +3 more
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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
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Nullspace Embeddings for Outerplanar Graphs [PDF]
, 2017 21 pages.
Lovász, L., Schrijver, A.
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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
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