Results 91 to 100 of about 1,320 (180)

Euler characteristics and chromatic polynomials

European Journal of Combinatorics, 2007
This work studies the relation between the chromatic polynomial of a graph \(G\) and the Euler characteristic of certain spaces. These spaces are obtained by a construction which is a generalization of the configuration space. The authors show, in the case that \(G\) has only one point, the following theorem: Let \(G\) be a graph and \(M_G\) the ...
Michael Eastwood, Stephen Huggett
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Approximating chromatic sum coloring of bipartite graphs in expected polynomial time

Труды Института системного программирования РАН, 2018
It is known that if P≠NP the sum coloring problem cannot be approximated within for some constant . We propose for arbitrary small an approximation scheme for this problem that works in expected polynomial time.
A. S. Asratian, N. N. Kuzyurin
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Two Chromatic Polynomial Conjectures

Journal of Combinatorial Theory, Series B, 1997
Let \(P(t)\) be the chromatic polynomial of a graph. It is shown that \(P(5)^{-1}P(6)^2 P(7)^{-1}\) can be arbitrarily small, disproving a conjecture of Welsh that \(P(t)^2\geq P(t- 1)P(t+1)\), and also disproving several other conjectures of Brenti.
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Chromatic polynomials with least coefficients

Discrete Mathematics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
José Rodríguez, Appajosyula Satyanarayana   +1 more
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Note on graphs colouring

Le Matematiche, 1992
In this paper, we give the maximal number of (k+r)-colouring of a graph with n vertices and chromatic number k. Also, we obtain the maximal values for chromatic polynomial of a graph.
Dănuţ Marcu
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A Matrix Method for Chromatic Polynomials

Journal of Combinatorial Theory, Series B, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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All proper colorings of every colorable BSTS(15) [PDF]

Computer Science Journal of Moldova, 2010
A Steiner System, denoted S(t,k,v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case
Jeremy Mathews, Brett Tolbert
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Polynomials related to chromatic polynomials

, 2020
For a simple graph $G$, let $χ(G,x)$ denote the chromatic polynomial of $G$. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations.
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Maximum chromatic polynomial of 3-chromatic blocks

Discrete Mathematics, 1997
This article continues the work done by the author in [Maximum chromatic polynomials of 2-connected graphs, J. Graph Theory 18, No. 4, 329-336 (1994; Zbl 0809.05046)]. In that paper it was shown that the 2-connected graph of order \(n\) with the greatest number \(P(G,3)\) of proper 3-colourings is \(C_n\) (and, for \(n=5\), \(K_{2,3}\)), and that \(K_ ...
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Chromatic Polynomials and Cryptographic Hashing on WIP-Quasigroup Structures

Journal of Mathematics
Cryptographic hash functions are indispensable for today’s information security because they secure data integrity, authentication and encrypted storage.
Mohammad Mazyad Hazzazi, Muhammad Nadeem, Muhammad Kamran, Komiljon Mustafoyev, Samuel Asefa Fufa   +4 more
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