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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Turán number of theta graphs
θ图 图兰数 图论
2023/4/26
Turán-type problem may be one of central problems in extremal graph theory. Particularly, the Turán number of a cycle attracts much attention. In this talk, we introduce a terminology, that is, theta ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Symmetry in Cayley graphs
凯莱图 对称性 图论
2023/4/27
Cayley graphs form an important class of vertex-transitive graphs, which have been the object of study for many decades. These graphs admit a group of automorphisms that acts regularly (sharply-transi...
COEULERIAN GRAPHS
COEULERIAN GRAPHS
2015/8/14
We suggest a measure of “Eulerianness” of a finite directed graph and define a class of “coEulerian” graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we...
Continuous-time distributed convex optimization on directed graphs
Continuous-time convex optimization directed graphs Optimization and Control
2012/4/17
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works ...
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Unsolved Problems Visibility Graphs of Points Segments Polygons
2011/3/3
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
A graph is K2,3-saturated if it has no subgraph isomorphic to K2,3, but does contain a K2,3 after the addition of any new edge. We prove that the minimum number of edges in a K2,3-saturated graph on n...
We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided K5 or a K−4 (= K4 with a single edge removed) as a subgraph. Together with a recent result of Ma and Yu tha...
The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided K5 .
The generalized connectivity of complete bipartite graphs
k-connectivity complete bipartite graph edge-disjoint spanning trees
2011/2/28
Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number ℓ of edge-disjoint trees T1, T2, . . . , T...
Cohen-Macaulayness of bipartite graphs, revisited
edge ideal of a graph Cohen-Macaulay bipartite graph
2011/1/17
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combi-natorial conditions for a bipart...
Distance-balanced closure of some graphs
Distances in graphs distance-balanced graphs distance-balanced closure
2011/2/22
In this paper we prove that any distance-balanced graph G with (G) |V (G)| − 3 is regular. Also we define notion of distance-balanced closure of a graph and we find distance-
balanced closur...
We study the commutation structure within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.
In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour,
and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of seve...
Small (2,s)-colorable graphs without 1-obstacle representations
Small (2,s)-colorable graphs 1-obstacle representations
2011/3/4
An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the mi...
Generalized Delaunay Graphs with respect to any Convex Set are Plane Graphs
Generalized Delaunay Graphs Convex Set Plane Graphs
2011/3/3
We consider two types of geometric graphs on point sets on the plane based on a plane set C: one obtained by translates of C, another by positively scaled translates (homothets) of C. For compact and ...