Results 261 to 270 of about 5,537,312 (288)

Coloring Powers of Planar Graphs

SIAM Journal on Discrete Mathematics, 2003
Summary: We give nontrivial bounds for the inductiveness or degeneracy of power graphs \(G^{k}\) of a planar graph \(G\). This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph.
Geir Agnarsson, Magnús M. Halldórsson
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Graphs whose powers are chordal and graphs whose powers are interval graphs

Journal of Graph Theory, 1997
The main theorem of this paper gives a forbidden induced subgraph condition on \(G\) that is sufficient for chordality of \(G^m\). This theorem is a generalization of a theorem of Balakrishnan and Paulraja who had provided this only for \(m=2\).
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Power graphs

J. Inf. Process. Cybern., 1994
Summary: Graphs with vertex set \(V\) can be ``lifted'' to the power set \(V^\#= {\mathcal P}(V)\backslash \{\varnothing\}\). In this paper graphs and their properties, in particular automorphisms and isomorphisms, are studied with respect to this power construction.
Ulrike Baumann, Reinhard Pöschel, Irmgard Schmeichel   +2 more
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The Chromatic Number of Graph Powers

Combinatorics, Probability and Computing, 2002
It is shown that the maximum possible chromatic number of the square of a graph with maximum degree d and girth g is (1 +o(1))d2 if g = 3, 4, 5 or 6, and is Θ(d2 / log d) if g [ges ] 7. Extensions to higher powers are considered as well.
Noga Alon, Bojan Mohar
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Unleashing the Power of Information Graphs

ACM SIGMOD Record, 2015
Information graphs are generic graphs that model different types of information through nodes and edges. Knowledge graphs are the most common type of information graphs in which nodes represent entities and edges represent relationships among them.
Matteo Lissandrini, Davide Mottin, Themis Palpanas, Dimitra Papadimitriou, Yannis Velegrakis   +4 more
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Powers of graphs

Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84, 1984
In this paper we investigate a powerful, and yet simple, technique for devising approximation algorithms for a wide variety of NP-complete problems in routing, location, and communication network design. Each of the algorithms presented here delivers an approximate solution guaranteed to be within a constant factor of the optimal solution. In addition,
Dorit S. Hochbaum, David B. Shmoys
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Coloring Powers of Chordal Graphs

SIAM Journal on Discrete Mathematics, 2004
Summary: We prove that the \(k\)th power \(G^{k}\) of a chordal graph \(G\) with maximum degree \(\Delta\) is \(O(\sqrt{k}\Delta^{(k+1)/2})\)-degenerate for even values of \(k\) and \(O(\Delta^{(k+1)/2})\)-degenerate for odd values. In particular, this bounds the chromatic number \(\chi(G^k)\) of the \(k\)th power of \(G\).
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Comparing the Power of Games on Graphs

Mathematical Logic Quarterly, 1997
AbstractThe descriptive complexity of a problem is the complexity of describing the problem in some logical formalism. One of the few techniques for proving separation results in descriptive complexity is to make use of games on graphs played between two players, called the spoiler and the duplicator. There are two types of these games, which differ in
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Applying Power Graph Analysis to Weighted Graphs

2012
We expanded Power Graph Analysis for use with weighted graphs, applying the technique to document categorisation with promising results. With the additional weight information we were able to create more accurate representations of the underlying data while maintaining a high level of edge reduction and improving visualisation of the graph.
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Between the enhanced power graph and the commuting graph

Journal of Graph Theory, 2023
Peter Cameron, Bojan Kuzma
exaly