Results 11 to 20 of about 42,715 (280)
On graphs double-critical with respect to the colouring number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The colouring number col($G$) of a graph $G$ is the smallest integer $k$ for which there is an ordering of the vertices of $G$ such that when removing the vertices of $G$ in the specified order no vertex of degree more than $k-1$ in the remaining graph ...
Matthias Kriesell, Anders Pedersen
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Acyclic, Star and Oriented Colourings of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let G be a graph with chromatic number χ (G). A vertex colouring of G is \emphacyclic if each bichromatic subgraph is a forest. A \emphstar colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χ _a(G) and χ _s(G)
David R. Wood
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Measurable versions of Vizing's theorem [PDF]
, 2020 We establish two versions of Vizing's theorem for Borel multi-graphs whose vertex degrees and edge multiplicities are uniformly bounded by respectively $\Delta$ and $\pi$.
Grebík, Jan, Pikhurko, Oleg
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On Small Balanceable, Strongly-Balanceable and Omnitonal Graphs
Discussiones Mathematicae Graph Theory, 2022 In Ramsey Theory for graphs we are given a graph G and we are required to find the least n0 such that, for any n ≥ n0, any red/blue colouring of the edges of Kn gives a subgraph G all of whose edges are blue or all are red.
Caro Yair, Lauri Josef, Zarb Christina
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Strong edge-colouring of sparse planar graphs [PDF]
, 2014 A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree $\Delta$ has a strong edge-colouring with at most $4\Delta+4$ colours. We show that $3\Delta+
Bensmail, Julien +3 more
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Every plane graph of maximum degree 8 has an edge-face 9-colouring [PDF]
, 2011 An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours.
Kang, Ross J. +2 more
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A note on the size Ramsey numbers for matchings versus cycles [PDF]
Mathematica Bohemica, 2021 For graphs $G$, $F_1$, $F_2$, we write $G \rightarrow(F_1, F_2)$ if for every red-blue colouring of the edge set of $G$ we have a red copy of $F_1$ or a blue copy of $F_2$ in $G$.
Edy Tri Baskoro, Tomáš Vetrík
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Vertex-Colouring Edge-Weightings
Combinatorica, 2007 A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv, is $${\sum\nolimits_{e \mathrel\backepsilon v} {w{\left( e \right)}} }$$. We show that the edges of every graph that does not contain a component isomorphic to K2 can be weighted from the set {1, . . .
Addario-Berry, L +4 more
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Line game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move. $Y\in\{A,B,-\}$.
Stephan Dominique Andres, Wai Lam Fong
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GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS
Ural Mathematical Journal, 2023 A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta +3 more
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