scholarly journals Gorenstein Polytopes Obtained from Bipartite Graphs

10.37236/280 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Makoto Tagami
Keyword(s):  
Perfect Matching ◽  
Infinite Family ◽  
Bipartite Graphs ◽  
Grid Graphs ◽  
New Class ◽  
Matching Polytopes

Beck et al. characterized the grid graphs whose perfect matching polytopes are Gorenstein and they also showed that for some parameters, perfect matching polytopes of torus graphs are Gorenstein. In this paper, we complement their result, that is, we characterize the torus graphs whose perfect matching polytopes are Gorenstein. Beck et al. also gave a method to construct an infinite family of Gorenstein polytopes. In this paper, we introduce a new class of polytopes obtained from graphs and we extend their method to construct many more Gorenstein polytopes.

Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting

2013 ◽  
Vol 22 (5) ◽  
pp. 783-799 ◽  
Author(s):  
GUILLEM PERARNAU ◽  
ORIOL SERRA
Keyword(s):  
Bipartite Graph ◽  
High Probability ◽  
Perfect Matching ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Asymptotic Enumeration ◽  
Complete Bipartite Graphs ◽  
Edge Colourings ◽  
Square Matrix

A perfect matchingMin an edge-coloured complete bipartite graphKn,nis rainbow if no pair of edges inMhave the same colour. We obtain asymptotic enumeration results for the number of rainbow perfect matchings in terms of the maximum number of occurrences of each colour. We also consider two natural models of random edge-colourings ofKn,nand show that if the number of colours is at leastn, then there is with high probability a rainbow perfect matching. This in particular shows that almost every square matrix of ordernin which every entry appearsntimes has a Latin transversal.

scholarly journals Space complexity of perfect matching in bounded genus bipartite graphs

2012 ◽  
Vol 78 (3) ◽  
pp. 765-779 ◽  
Author(s):  
Samir Datta ◽  
Raghav Kulkarni ◽  
Raghunath Tewari ◽  
N.V. Vinodchandran
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs ◽  
Space Complexity

scholarly journals Differentials in certain classes of graphs

2010 ◽  
Vol 41 (2) ◽  
pp. 129-138 ◽  
Author(s):  
P. Roushini Leely Pushpam ◽  
D. Yokesh
Keyword(s):  
Binary Tree ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Regular Graphs ◽  
Complete Binary Tree ◽  
Unicyclic Graphs ◽  
Grid Graphs ◽  
Split Graphs ◽  
Delta G

Let $X subset V$ be a set of vertices in a graph $G = (V, E)$. The boundary $B(X)$ of $X$ is defined to be the set of vertices in $V-X$ dominated by vertices in $X$, that is, $B(X) = (V-X) cap N(X)$. The differential $ partial(X)$ of $X$ equals the value $ partial(X) = |B(X)| - |X|$. The differential of a graph $G$ is defined as $ partial(G) = max { partial(X) | X subset V }$. It is easy to see that for any graph $G$ having vertices of maximum degree $ Delta(G)$, $ partial(G) geq Delta (G) -1$. In this paper we characterize the classes of unicyclic graphs, split graphs, grid graphs, $k$-regular graphs, for $k leq 4$, and bipartite graphs for which $ partial(G) = Delta(G)-1$. We also determine the value of $ partial(T)$ for any complete binary tree $T$.

A CHARACTERIZATION OF PM-COMPACT CLAW-FREE CUBIC GRAPHS

2014 ◽  
Vol 06 (02) ◽  
pp. 1450025 ◽  
Author(s):  
XIUMEI WANG ◽  
WEIPING SHANG ◽  
YIXUN LIN ◽  
MARCELO H. CARVALHO
Keyword(s):  
Convex Hull ◽  
Perfect Matching ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Matching Polytopes ◽  
Matching Polytope

The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. This paper characterizes claw-free cubic graphs whose 1-skeleton graphs of perfect matching polytopes have diameter 1.

A new class of heuristic algorithms for weighted perfect matching

1988 ◽  
Vol 35 (4) ◽  
pp. 769-776 ◽  
Author(s):  
M. D. Grigoriadis ◽  
B. Kalantari
Keyword(s):  
Perfect Matching ◽  
Heuristic Algorithms ◽  
New Class
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