scholarly journals The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite Claw

2021 ◽  
Author(s):  
Ilia Ponomarenko ◽  
Grigory Ryabov
Keyword(s):  
Bipartite Graphs ◽  
Chordal Bipartite Graphs

scholarly journals Acyclic homomorphisms to stars of graph Cartesian products and chordal bipartite graphs

2012 ◽  
Vol 312 (14) ◽  
pp. 2146-2152
Author(s):  
Mieczysław Borowiecki ◽  
Ewa Drgas-Burchardt
Keyword(s):  
Bipartite Graphs ◽  
Cartesian Products ◽  
Chordal Bipartite Graphs

scholarly journals Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

2005 ◽  
Vol 145 (3) ◽  
pp. 479-482 ◽  
Author(s):  
Ryuhei Uehara ◽  
Seinosuke Toda ◽  
Takayuki Nagoya
Keyword(s):  
Graph Isomorphism ◽  
Bipartite Graphs ◽  
Chordal Graphs ◽  
Strongly Chordal Graphs ◽  
Chordal Bipartite Graphs

Fast and simple algorithms for counting dominating sets in distance-hereditary graphs

2020 ◽  
pp. 2150012
Author(s):  
Min-Sheng Lin
Keyword(s):  
Linear Time ◽  
Bipartite Graphs ◽  
Chordal Graphs ◽  
Dominating Sets ◽  
Complete Problem ◽  
Split Graphs ◽  
Linear Time Algorithms ◽  
Chordal Bipartite Graphs

Counting dominating sets (DSs) in a graph is a #P-complete problem even for chordal bipartite graphs and split graphs, which are both subclasses of weakly chordal graphs. This paper investigates this problem for distance-hereditary graphs, which is another known subclass of weakly chordal graphs. This work develops linear-time algorithms for counting DSs and their two variants, total DSs and connected DSs in distance-hereditary graphs.

scholarly journals Complexity of Hamiltonian Cycle Reconfiguration

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 140 ◽  
Author(s):  
Asahi Takaoka
Keyword(s):  
Hamiltonian Cycle ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Interval Graph ◽  
Unit Interval ◽  
Chordal Graphs ◽  
Hamiltonian Cycles ◽  
Permutation Graph ◽  
Proper Subclass ◽  
Chordal Bipartite Graphs

The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained from C i − 1 by a switch for each i with 1 ≤ i ≤ t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time.

COMPLEXITY OF CERTAIN FUNCTIONAL VARIANTS OF TOTAL DOMINATION IN CHORDAL BIPARTITE GRAPHS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250045 ◽  
Author(s):  
D. PRADHAN
Keyword(s):  
Dominating Set ◽  
Bipartite Graphs ◽  
Total Domination ◽  
Fixed Integer ◽  
Functional Variants ◽  
Total Dominating Set ◽  
Domination Problem ◽  
Signed Total Domination ◽  
The Cost ◽  
Chordal Bipartite Graphs

In this paper, we consider minimum total domination problem along with two of its variations namely, minimum signed total domination problem and minimum minus total domination problem for chordal bipartite graphs. In the minimum total domination problem, the objective is to find a smallest size subset TD ⊆ V of a given graph G = (V, E) such that |TD∩NG(v)| ≥ 1 for every v ∈ V. In the minimum signed (minus) total domination problem for a graph G = (V, E), it is required to find a function f : V → {-1, 1} ({-1, 0, 1}) such that f(NG(v)) = ∑u∈NG(v)f(u) ≥ 1 for each v ∈ V, and the cost f(V) = ∑v∈V f(v) is minimized. We first show that for a given chordal bipartite graph G = (V, E) with a weak elimination ordering, a minimum total dominating set can be computed in O(n + m) time, where n = |V| and m = |E|. This improves the complexity of the minimum total domination problem for chordal bipartite graphs from O(n2) time to O(n + m) time. We then adopt a unified approach to solve the minimum signed (minus) total domination problem for chordal bipartite graphs in O(n + m) time. The method is also able to solve the minimum k-tuple total domination problem for chordal bipartite graphs in O(n + m) time. For a fixed integer k ≥ 1 and a graph G = (V, E), the minimum k-tuple total domination problem is to find a smallest subset TDk ⊆ V such that |TDk ∩ NG(v)| ≥ k for every v ∈ V.

scholarly journals Biclique edge-choosability in some classes of graphs∗

2017 ◽  
Author(s):  
Gabriel A. G. Sobral ◽  
Marina Groshaus ◽  
André L. P. Guedes
Keyword(s):  
Lower Bound ◽  
Edge Coloring ◽  
Bipartite Graphs ◽  
Polynomial Algorithms ◽  
Odd Cycles ◽  
Chordal Bipartite Graphs

In this paper we study the problem of coloring the edges of a graph for any k-list assignment such that there is no maximal monochromatic biclique, in other words, the k-biclique edge-choosability problem. We prove that the K3free graphs that are not odd cycles are 2-star edge-choosable, chordal bipartite graphs are 2-biclique edge-choosable and we present a lower bound for the biclique choice index of power of cycles and power of paths. We also provide polynomial algorithms to compute a 2-biclique (star) edge-coloring for K3-free and chordal bipartite graphs for any given 2-list assignment to edges.

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