Results 31 to 40 of about 5,178 (231)
On Proper (Strong) Rainbow Connection of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored graph G is called a rainbow path if no two edges on the path have the same color. The graph G is called rainbow connected if between every pair of distinct vertices of G, there is a rainbow path.
Jiang Hui +3 more
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Strong edge colorings of uniform graphs
Discrete Mathematics, 2004 A strong edge coloring of a graph is a (proper) edge coloring in which every color class is an induced matching. The strong chromatic index \(\chi_S(G)\) of a graph \(G\) is the minimum number of colors in a strong edge coloring of \(G\). For a bipartite graph \(G=(U\cup V, E)\), and for two nonempty sets \(U'\subseteq U\) and \(V'\subseteq V\), let ...
Andrzej Czygrinow, Brendan Nagle
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Some Equal Degree Graph Edge Chromatic Number
MATEC Web of Conferences, 2016 Let G(V, E) be a simple graph and k is a positive integer, if it exists a mapping of f, and satisfied with f(e1)≠6 = f(e2) for two incident edges e1,e2∉E(G), f(e1)≠6=f(e2), then f is called the k-proper-edge coloring of G(k-PEC for short).
Liu Jun +4 more
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The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
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Strong Chromatic Index Of Planar Graphs With Large Girth
Discussiones Mathematicae Graph Theory, 2014 Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of ...
Jennhwa Chang Gerard +3 more
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Incidence and strong edge colorings of graphs
Discrete Mathematics, 1993 The incidence coloring number of a graph is defined and bounded in terms of the maximum degree. The incidence coloring number turns out to be the strong chromatic index of an associated bipartite graph. A bound for the strong chromatic index of bipartite graphs all of whose cycle lengths are divisible by 4 is improved.
Richard A. Brualdi +1 more
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Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Discussiones Mathematicae Graph Theory, 2013 We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Borodin Oleg V., Ivanova Anna O.
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Upper Bounds for the Strong Chromatic Index of Halin Graphs
Discussiones Mathematicae Graph Theory, 2018 The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2.
Hu Ziyu, Lih Ko-Wei, Liu Daphne Der-Fen
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Color code techniques in rainbow connection
Electronic Journal of Graph Theory and Applications, 2018 Let G be a graph with an edge k-coloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors.
Fendy Septyanto, Kiki A. Sugeng
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FEBS Letters, EarlyView.In this study, we found that human cervical‐derived adipocytes maintain intracellular iron level by regulating the expression of iron transport‐related proteins during adrenergic stimulation. Melanotransferrin is predicted to interact with transferrin receptor 1 based on in silico analysis.
Rahaf Alrifai +9 more
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