Results 21 to 30 of about 138,741 (178)
Relaxed Two-Coloring of Cubic Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show that any graph of maximum degree at most $3$ has a two-coloring, such that one color-class is an independent set while the other color induces monochromatic components of order at most $189$. On the other hand for any constant $C$ we exhibit a $4$
Robert Berke, Tibor Szabó
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New Concepts of Vertex Covering in Cubic Graphs with Its Applications
Mathematics, 2022 Graphs serve as one of the main tools for the mathematical modeling of various human problems. Fuzzy graphs have the ability to solve uncertain and ambiguous problems.
Huiqin Jiang +4 more
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Infinite families of asymmetric graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G is asymmetric if its automorphism group of vertices is trivial. Asymmetric graphs were introduced by Erdős and Rényi in 1963. They showed that the probability of a graph on n vertices being asymmetric tends to 1 as n tends to infinity.
Alejandra Brewer +5 more
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Constructing Minimally 3-Connected Graphs
Algorithms, 2021 A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an ...
João Paulo Costalonga +2 more
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Colourings of cubic graphs inducing isomorphic monochromatic subgraphs [PDF]
, 2018 A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what ...
Bondy J. A. +6 more
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Cubic Graphs and Their Application to a Traffic Flow Problem
International Journal of Computational Intelligence Systems, 2020 A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems.
G. Muhiuddin +3 more
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Maker-Breaker total domination game on cubic graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We study Maker--Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing the role of Maker) wins if she manages to claim an open neighbourhood of a vertex. Dominator wins otherwise (i.e.\
Jovana Forcan, Mirjana Mikalački
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Cuts in matchings of 3-connected cubic graphs [PDF]
, 2018 We discuss conjectures on Hamiltonicity in cubic graphs (Tait, Barnette, Tutte), on the dichromatic number of planar oriented graphs (Neumann-Lara), and on even graphs in digraphs whose contraction is strongly connected (Hochst\"attler). We show that all
Knauer, Kolja, Valicov, Petru
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On measures of nonplanarity of cubic graphs
Pracì Mìžnarodnogo Geometričnogo Centru, 2018 We study two measures of nonplanarity of cubic graphs G, the genus γ (G), and the edge deletion number ed(G). For cubic graphs of small orders these parameters are compared with another measure of nonplanarity, the rectilinear crossing number (G).
Leonid Plachta
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On parsimonious edge-colouring of graphs with maximum degree three [PDF]
, 2012 In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed that $\gamma \geq 13/15$ when $G$ is cubic . We show here that this result can be extended to graphs
Fouquet, Jean-Luc, Vanherpe, Jean-Marie
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