Finding minimum height elimination trees for interval graphs in polynomial time

1994 ◽  
Vol 34 (4) ◽  
pp. 484-509 ◽  
Author(s):  
Bengt Aspvall ◽  
Pinar Heggernes
Keyword(s):  
Polynomial Time ◽  
Interval Graphs ◽  
Minimum Height

Solving the maximum internal spanning tree problem on interval graphs in polynomial time

2018 ◽  
Vol 734 ◽  
pp. 32-37
Author(s):  
Xingfu Li ◽  
Haodi Feng ◽  
Haotao Jiang ◽  
Binhai Zhu
Keyword(s):  
Polynomial Time ◽  
Spanning Tree ◽  
Interval Graphs

scholarly journals Computing the Weighted Isolated Scattering Number of Interval Graphs in Polynomial Time

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Fengwei Li ◽  
Xiaoyan Zhang ◽  
Qingfang Ye ◽  
Yuefang Sun
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Interval Graphs ◽  
Perfect Graphs ◽  
Network Vulnerability ◽  
Hamiltonian Properties

The scattering number and isolated scattering number of a graph have been introduced in relation to Hamiltonian properties and network vulnerability, and the isolated scattering number plays an important role in characterizing graphs with a fractional 1-factor. Here we investigate the computational complexity of one variant, namely, the weighted isolated scattering number. We give a polynomial time algorithm to compute this parameter of interval graphs, an important subclass of perfect graphs.

scholarly journals Chromatic Polynomials of Oriented Graphs

10.37236/8240 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Danielle Cox ◽  
Christopher Duffy
Keyword(s):  
Polynomial Time ◽  
Open Problem ◽  
Oriented Graph ◽  
Chromatic Polynomial ◽  
Simple Graph ◽  
Interval Graphs ◽  
Chromatic Polynomials ◽  
Oriented Graphs ◽  
Real Roots ◽  
The Family

The oriented chromatic polynomial of a oriented graph outputs the number of oriented $k$-colourings for any input $k$. We fully classify those oriented graphs for which the oriented graph has the same chromatic polynomial as the underlying simple graph, closing an open problem posed by Sopena. We find that such oriented graphs can be both identified and constructed in polynomial time as they are exactly the family of quasi-transitive oriented co-interval graphs. We study the analytic properties of this polynomial and show that there exist oriented graphs which have chromatic polynomials have roots, including negative real roots,  that cannot be realized as the root of any chromatic polynomial of a simple graph.

scholarly journals Isolated Scattering Number Can be Computed in Polynomial Time for Interval Graphs

2017 ◽  
Vol 58 ◽  
pp. 81 ◽  
Author(s):  
Fengwei Li ◽  
Qingfang Ye ◽  
Yuefang Sun
Keyword(s):  
Polynomial Time ◽  
Interval Graphs

scholarly journals Computing role assignments of proper interval graphs in polynomial time

2012 ◽  
Vol 14 ◽  
pp. 173-188 ◽  
Author(s):  
Pinar Heggernes ◽  
Pim van ʼt Hof ◽  
Daniël Paulusma
Keyword(s):  
Polynomial Time ◽  
Interval Graphs
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