A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A note on the interval number of a graph

1985
*
Discrete Mathematics
*

Acknowledgment We thank

doi:10.1016/0012-365x(85)90041-x
fatcat:xcx644veljgmrn65vpl62bdmji
*the*referees for strengthening Theorem 2 for m 23. ... In this*note*, we apply counting arguments and results*on**graph*decomposition to obtain inequalities concerning*the**interval**number**of**a**graph*G. ... Such*a*description*of*G is called*a*t-representation*of*6. Extremal results*on**the**interval**number**of**a**graph*have given us upper bounds*on*i(G) in terms*of*other*graph*parameters; see Table 1 . ...##
###
Reconstruction of Interval Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

Since

doi:10.1007/978-3-642-02882-3_12
fatcat:dla5mepni5fxfdimqs7oeyjvme
*the**number**of**interval**graphs*that can be obtained from an*interval**graph*by adding*a*vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE ...*The**graph*reconstruction conjecture is*a*long-standing open problem in*graph*theory. ...*Note*that*the**number**of*maximal cliques in an n-vertex*interval**graph*is at most n (see [4] ). Lemma 6. All*the*compact*interval*representations*of*an*interval**graph*have*the*same length. ...##
###
The total interval number of a graph, I: Fundamental classes

1993
*
Discrete Mathematics
*

West,

doi:10.1016/0012-365x(93)90057-z
fatcat:o56vfrq4u5fabkrfjdy6lfspzu
*The*total*interval**number**of**a**graph*, I: Fundamental classes, Discrete Mathematics 118 (1993) 145-156. ...*The*total interual*number*I(G) is*the*minimum*of**the*total*number**of**intervals*used in any such representation*of*G. ... Then i(G) = min,,,F max, t VCG, #f(*a*) is called*the**interval**number**of*G;*the**interval**graphs*are*the**graphs*with*interval**number*1. ...##
###
Reconstruction of interval graphs

2010
*
Theoretical Computer Science
*

Since

doi:10.1016/j.tcs.2010.07.006
fatcat:v4q7tze7xzg3pnddm66wkxvrgm
*the**number**of**interval**graphs*that can be obtained from an*interval**graph*by adding*a*vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE ...*The**graph*reconstruction conjecture is*a*long-standing open problem in*graph*theory. ...*Note*that*the**number**of*maximal cliques in an n-vertex*interval**graph*is at most n (see [4] ). Lemma 6. All*the*compact*interval*representations*of*an*interval**graph*have*the*same length. ...##
###
On a special class of boxicity 2 graphs
[article]

2016
*
arXiv
*
pre-print

We define and study

arXiv:1603.09561v1
fatcat:phzx2lo6dbardfzll7nvwny2vy
*a*class*of**graphs*, called 2-stab*interval**graphs*(2SIG), with boxicity 2 which properly contains*the*class*of**interval**graphs*. ... It turns out that for these kind*of**graphs*,*the*chromatic*number**of*any*of*its induced subgraphs is bounded by twice*of*its (induced subgraph) clique*number*. ...*Note*that G[V 1 ] and G[V 2 ] are unit*interval**graphs*. We prove*the*statement using induction*on*clique*number*ω(G).*Note*that*the*theorem is true for*graphs*G with ω(G) = 2 by Lemma 4.8. ...##
###
On Interval Non-Edge-Colorable Eulerian Multigraphs
[article]

2013
*
arXiv
*
pre-print

In this

arXiv:1311.2210v2
fatcat:onot6bycgjez5d2cz4k5ugwwpu
*note*, we show that all Eulerian multigraphs with an odd*number**of*edges have no*interval*coloring. ... ,t is called an*interval*t-coloring if all colors are used, and*the*colors*of*edges incident to any vertex*of*G are distinct and form an*interval**of*integers. ... For*a**graph*G, by L(G) we denote*the*line*graph**of**the**graph*G. We also need*a*classical result*on*Eulerian multigraphs. ...##
###
Folkmusic and computers

1968
*
African Music: Journal of the African Music Society
*

If

doi:10.21504/amj.v4i2.784
fatcat:gslhgk4jdbaaberlyscxyt3lze
*the*final*note*is flat*of**the*octave,*the*vps*number*will be less than twice that*of**the*tonic,*the*factors will be unequal, and*the**note*will fall short*of**the*last position*on**the**graph*, as in*graph*...*The*process is repeated for each subsequent*note*until*the*octave is reached, giving*a*result*of*nought*on*subtraction since*the*vps*number**of**the*octave is exactly twice that*of**the*tonic, and both have ...*The**interval*between*a**note*and*the*tonic is found by adding together all*the**intervals**of**the*intermediate*notes*. ...##
###
Coloring Clean and K 4-Free Circle Graphs
[chapter]

2012
*
Thirty Essays on Geometric Graph Theory
*

*A*circle

*graph*is

*the*intersection

*graph*

*of*chords drawn in

*a*circle.

*The*best known general upper bound

*on*

*the*chromatic

*number*

*of*circle

*graphs*with clique

*number*k is 50 · 2 k . ... Based

*on*this result we prove that

*the*chromatic

*number*

*of*every circle

*graph*with clique

*number*at most 3 is at most 38. ...

*The*above-mentioned complexity results

*on*circle

*graphs*make interesting upper bounds

*on*

*the*chromatic

*number*

*of*circle

*graphs*in terms

*of*their clique

*number*, especially if

*the*proofs yield polynomial ...

##
###
Coloring Fuzzy Circular Interval Graphs

2009
*
Electronic Notes in Discrete Mathematics
*

*The*algorithm reduces

*the*problem to

*the*case

*of*circular

*interval*

*graphs*, then making use

*of*

*a*coloring algorithm by Gijswijt. ... We provide

*a*polynomial time combinatorial algorithm that computes

*the*weighted coloring

*number*and

*the*corresponding colorings for fuzzy circular

*interval*

*graphs*. ... If both endpoints have at least

*one*node, we have

*a*fuzzy pair. Let be

*the*

*number*

*of*fuzzy pairs.

*Note*that ≤ |V (G)| as fuzzy pairs are disjoint. ...

##
###
The harmonious coloring problem is NP-complete for interval and permutation graphs

2007
*
Discrete Applied Mathematics
*

Given

doi:10.1016/j.dam.2007.07.005
fatcat:iil7nbeolnai3nmjgar3nffcfa
*a*simple*graph*G,*a*harmonious coloring*of*G is*a*proper vertex coloring such that each pair*of*colors appears together*on*at most*one*edge. ... Extending previous work*on**the*NP-completeness*of**the*harmonious coloring problem when restricted to*the*class*of*disconnected*graphs*which are simultaneously cographs and*interval**graphs*, we prove that ...*One*can easily verify that G is an*interval**graph*.*A*clique can be represented as*a**number**of**intervals*that share at least*one*point in common. ...##
###
The interval number of a planar graph: Three intervals suffice

1983
*
Journal of combinatorial theory. Series B (Print)
*

*The*

*interval*

*number*i(G)

*of*

*a*

*graph*G is

*the*smallest

*number*t such that G has

*a*t-

*interval*representation. It is proved that i(G) < 3 whenever G is planar and that this bound is

*the*best possible. ... Suppose each vertex

*of*

*a*

*graph*G is assigned

*a*subset

*of*

*the*real line consisting

*of*at most t closed

*intervals*. ... He

*noted*that

*the*

*interval*

*number*

*of*

*a*

*graph*is at most

*one*more than its arboricity, which is

*the*minimum

*number*

*of*spanning forests needed to partition its edges. ...

##
###
Coloring fuzzy circular interval graphs

2012
*
European journal of combinatorics (Print)
*

*The*algorithm reduces

*the*problem to

*the*case

*of*circular

*interval*

*graphs*, then making use

*of*

*a*coloring algorithm by Gijswijt. ... We provide

*a*polynomial time combinatorial algorithm that computes

*the*weighted coloring

*number*and

*the*corresponding colorings for fuzzy circular

*interval*

*graphs*. ... If both endpoints have at least

*one*node, we have

*a*fuzzy pair. Let be

*the*

*number*

*of*fuzzy pairs.

*Note*that ≤ |V (G)| as fuzzy pairs are disjoint. ...

##
###
A Note on Online Colouring Problems in Overlap Graphs and Their Complements
[chapter]

2018
*
Lecture Notes in Computer Science
*

Our method is based

doi:10.1007/978-3-319-75172-6_13
fatcat:tvfd3refxrb6lgc6ay7wlqvdse
*on**a*partition*of**the*overlap*graph*into permutation*graphs*, leading to*a*competitive-preserving reduction*of**the*problem in overlap*graphs*to*the*same problem in permutation*graphs*... An instance is*a*system*of*time*intervals*presented in non-decreasing order*of**the*left endpoints. ... Acknowledgments*The*authors would like to thank anonymous referees for their helpful comments. ...##
###
A register allocation framework based on hierarchical cyclic interval graphs
[chapter]

1992
*
Lecture Notes in Computer Science
*

In this paper, we present

doi:10.1007/3-540-55984-1_17
fatcat:mlli3y7ktvbrbjnyezb6muyzw4
*a*new register allocation framework based*on*hierarchical cyclic*interval**graphs*. ... In addition, we present*a*spilling algorithm that makes use*of**the*extra information available in*the**interval**graph*representation. ...*Note*that*the*lifetimes*of*each variable are represented by*a*sequence*of**intervals*,*one**interval*for each iteration. ...##
###
Random Generation and Enumeration of Proper Interval Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

( ( ) ( ( ) ) ( ) ) Proper

doi:10.1007/978-3-642-00202-1_16
fatcat:btlcfczav5g3joridqmqxwwezq
*Interval**Graph*Unit*Interval*Rep. ( ( ) ( ( ) ) ( ) ) reversible This*graph*has only*one*string representation. ... Huang, 1996) *A*connected P. I. G. has only*one*or two string rep.( ( ) ( ( ) ( ) ) )Proper*Interval**Graph*Unit*Interval*Rep. String Rep. Lemma 1.(X. Dell, P. Hell, J. ...
« Previous

*Showing results 1 — 15 out of 664,369 results*