A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On the complexity of finding the chromatic number of a recursive graph II: the unbounded case

1989
*
Annals of Pure and Applied Logic
*

We show that

doi:10.1016/0168-0072(89)90037-7
fatcat:e6wj33qzebbwld2pv2refc2lhe
*the*problem*of*determining*the**chromatic**number**of**a**recursive**graph*with*a*minimum*number**of*queries to*the*halting set. is close$ related to*the**unbounded*search problem. ... queries to*a*less powerful set atic*number*, and 8" & Y when computhope*of*cutting down*on**the**number**of**The*most substantial savings*of*queries occurs in*the*problem*recursive**chromatic**number**of**a*highly ... In this section we show that if f(n) queries suffice to solve*the**unbounded*search problem, then f(n) queries can be used to*find**the**chromatic**number**of**a**recursive**graph*; and conversely that if d(n) ...##
###
On the complexity of finding the chromatic number of a recursive graph I: the bounded case

1989
*
Annals of Pure and Applied Logic
*

We will be concerned with

doi:10.1016/0168-0072(89)90029-8
fatcat:kkh3waxg55e5llsmw7cmya5jiy
*finding**the**chromatic**number**of**a**graph*when that*number*is*a*priori bounde above by*a*constant.*Unbounded*versions*of*problems in tlris r are studied in [ 111. ... In particular, (p + l)-ary search is not always optimal for*finding**the**chromatic**number**of**a**recursive**graph*. ... Gasmh any*A*, to compute # (i)*Recursive*grdzphs 0*ii**recursive**graphs*c odd log(c + 1) -1 WP + 1) @Wandcodd c even c eve*The**complexity*ofjlnding*the**chromatic**number*31 (b) Using ...##
###
Graph polynomials and their applications II: Interrelations and interpretations
[article]

2008
*
arXiv
*
pre-print

This paper surveys

arXiv:0806.4699v1
fatcat:4qzf6mxhsrgqzkgcz4xm2jimau
*a*comprehensive, although not exhaustive, sampling*of**graph*polynomials with*the*goal*of*providing*a*brief overview*of**a*variety*of*techniques defining*a**graph*polynomial and then for ... We conclude with two examples,*one*from biology and*one*from physics, that illustrate*the*applicability*of**graph*polynomials in other fields. ... To compute P (G; x), let G be*a*plane*graph*, and let G m be its medial*graph*, face two-colored with*the**unbounded*face colored white. ...##
###
Page 2994 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
*
Mathematical Reviews
*

We show that

*the*problem*of*determining*the**chromatic**number**of**a**recursive**graph*, with*a*minimum*number**of*queries to*the*halting set, is closely related to*the**unbounded*search problem. ...*II*.*The**unbounded**case*. Ann. Pure Appl. Logic 45 (1989), no. 3, 227-246. ...##
###
Independent sets in edge-clique graphs II
[article]

2013
*
arXiv
*
pre-print

We show that

arXiv:1206.5082v2
fatcat:om42b4o6j5b5rl62fmq4zygosu
*the*independent set problem*on*edge-clique*graphs**of*cographs. We show that*the*independent set problem*on*edge-clique*graphs**of**graphs*without odd wheels remains NP-complete. ... We show that edge-clique*graphs**of*cocktail party*graphs*have*unbounded*rankwidth. This, and other observations lead us to conjecture that*the*edge-clique cover problem is NP-complete for cographs. ... For general anti-Gallai*graphs**the*computation*of**the*clique*number*and*chromatic**number*are NP-complete. Let us mention that*the*recognition*of*anti-Gallai*graphs*is NP-complete. ...##
###
Book announcements

1990
*
Discrete Applied Mathematics
*

*The*cardinaiity

*of*

*a*

*recursively*defined set. Transformation

*of*

*a*

*number*

*of*definitions into

*one*-jamming. ... Chapter 3: Parity and

*One*-in-

*a*-box Predicates. Chapter 4:

*The*"And/Or" Theorem. PART

*II*: GEOMETRIC THEORY

*OF*LINEAR INEQUALITIES. Chapter 5: vCoNNECTED:

*A*Geometric Property with

*Unbounded*Order. ...

##
###
Master index to volumes 41-50

1990
*
Annals of Pure and Applied Logic
*

infinite paths Beigel, R. and Gasarch, W.I.,

doi:10.1016/0168-0072(90)90061-6
fatcat:inapyhmvyffpzkhhdq4qje4ahi
*On**the**complexity**of**finding**the**chromatic**number**of**a**recursive**graph*I:*the*bounded*case*Beigel, R. and Gasarch, W.I.,*On**the**complexity**of**finding**the**chromatic*...*number**of**a**recursive**graph**II*:*the**unbounded*Burke, M.R. and Magidor, M., Shelah's pcf theory and its applications Chong, CT., Hyperhypersimple sets and AZ systems Chong, C.T. and Downey, R.G., Minimal ...##
###
Binary search and recursive graph problems

1997
*
Theoretical Computer Science
*

*A*

*graph*G = (V, E) is

*recursive*if every node

*of*G has

*a*finite

*number*

*of*neighbors, and both V and E are

*recursive*(i.e., decidable). ... bounded and in

*the*

*unbounded*

*case*. ... Acknowledgements

*The*authors would like to thank Steven Lempp for helpful discussions, and

*the*anonymous referees for useful observations. ...

##
###
Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory
[article]

2021
*
arXiv
*
pre-print

Counting homomorphisms from

arXiv:1907.03850v2
fatcat:rg3upoulmve7jlsnloszbm22zu
*a**graph*H into another*graph*G is*a*fundamental problem*of*(parameterized) counting*complexity*theory. ... Our main result is*a*construction based*on*Kneser*graphs*that associates every problem P in #𝖶[1] with two classes*of**graphs*ℋ and 𝒢 such that*the*problem P is equivalent to*the*problem # HOM(ℋ→𝒢)*of*... Acknowledgements We thank Karl Bringmann and Holger Dell for fruitful discussions and valuable feedback*on*early drafts*of*this work. ...##
###
Ground-state degeneracy of Potts antiferromagnets: homeomorphic classes with noncompact W boundaries

1999
*
Physica A: Statistical Mechanics and its Applications
*

We present exact calculations

doi:10.1016/s0378-4371(98)00568-8
fatcat:mobfxc5a6nhy5a2mviz2jwqt7m
*of**the*zero-temperature partition function Z(G,q,T=0) and ground-state degeneracy W({G},q) for*the*q-state Potts antiferromagnet*on**a**number**of*families*of**graphs*G for which ... (generalizing q from Z_+ to C)*the*boundary B*of*regions*of*analyticity*of*W in*the**complex*q plane is noncompact, passing through z=1/q=0. ...*Of*course, since for finite r,*the**chromatic*polynomial is*of*finite degree (equal to*the**number**of*vertices*on**the**graph*), its zeros (i.e.,*the**chromatic*zeros*of**the**graph*) are*of*bounded magnitude in ...##
###
Book announcements

1991
*
Discrete Applied Mathematics
*

*The*MSCCC queueing discipline). Reversible queueing networks. Applications

*of*queueing network models (Queueing network models

*of*computer systems. ... Queueing network model

*of*

*a*distributed computer system. Queueing network models

*of*communication networks. Queueing model

*of*

*a*network

*of*workstations. Queueing model

*of*

*a*circuit-switched network. ... Fundamental set

*of*cycles. Cut Chapter 3: Traversability. Euler circuit. Hamiltonian cycle. Chapter 4: Node Coloring.

*Chromatic*

*number*.

*Chromatic*polynomial. Chapter 5: Minimum Spanning Tree. ...

##
###
Chromatic transitions in the emergence of syntax networks
[article]

2018
*
arXiv
*
pre-print

Here we explore

arXiv:1807.09194v1
fatcat:ihkhflmji5f6pc5c6cj3s345bq
*the*evolution*of*syntax networks through language acquisition using*the**chromatic**number*, which captures*the*transition and provides*a*natural link to standard theories*on*syntactic structures ... In*a*more general level, we observe that*the**chromatic*classes define independent regions*of**the**graph*, and thus, can be interpreted as*the*footprints*of*incompatibility relations, somewhat as opposed ... Acknowledgments We thank*Complex*Systems Lab members for fruitful conversations. This work was supported by*the*James McDonnell Foundation (BCM, SV, RSV) and*the*EU program FP7-ICT-270212 (MSF). ...##
###
Acyclic and star colorings of cographs

2011
*
Discrete Applied Mathematics
*

We also show that

doi:10.1016/j.dam.2011.04.011
fatcat:g2uep2reuvad5ar62d3pf6tt7u
*the*acyclic*chromatic**number*,*the*star*chromatic**number*,*the*treewidth plus 1, and*the*pathwidth plus 1 are all equal for cographs. ...*A*great deal*of**graph*-theoretical research has been conducted*on*acyclic and star coloring since they were introduced in*the*early seventies by Grünbaum [18] . ...*The*majority*of*this work was conducted when*the*author was employed by*The*University*of*Chicago and Argonne National Laboratory, supported in part by US Department*of*Energy under Contract DE-AC02-06CH11357 ...##
###
Acyclic and Star Colorings of Cographs
[article]

2011
*
arXiv
*
pre-print

We also show that

arXiv:1103.5531v1
fatcat:kbsfhq6idfccpouvcs3jlog4hy
*the*acyclic*chromatic**number*,*the*star*chromatic**number*,*the*treewidth plus*one*, and*the*pathwidth plus*one*are all equal for cographs. ... If*the**graph*is given in*the*form*of**a*cotree,*the*algorithm runs in O(n) time. ...*The*majority*of*this work was conducted when*the*author was employed by*The*University*of*Chicago and Argonne National Laboratory, supported in part by U.S. ...##
###
Disjointness graphs of short polygonal chains
[article]

2021
*
arXiv
*
pre-print

It is known that

arXiv:2112.05991v1
fatcat:4rlll6bgqfbbjnhvhnluywryse
*the*disjointness*graph*G*of*any system*of*segments in*the*plane is χ-bounded, that is, its*chromatic**number*χ(G) is upper bounded by*a*function*of*its clique*number*ω(G). ...*The*disjointness*graph**of**a*set system is*a**graph*whose vertices are*the*sets, two being connected by an edge if and only if they are disjoint. ... To prove Theorem 1, we established that*the*shift*graph*S n ,*a*triangle-free*graph**of**unbounded**chromatic**number*, can be obtained as*the*disjointness*graph**of*V-shapes. ...
« Previous

*Showing results 1 — 15 out of 401 results*