71views more  JCT 2011»
8 years 7 months ago
Pseudograph associahedra
Given a simple graph G, the graph associahedron KG is a simple polytope whose face poset is based on the connected subgraphs of G. This paper defines and constructs graph associah...
Michael Carr, Satyan L. Devadoss, Stefan Forcey
89views more  DM 1999»
8 years 11 months ago
On the distribution of eigenvalues of graphs
Let G be a simple graph with n( 2) vertices, and i(G) be the ith largest eigenvalue of G. In this paper we obtain the following: If 3(G) < 0, and there exists some index k, 2 ...
Alexander K. Kelmans, Xuerong Yong
134views more  ENDM 2002»
8 years 11 months ago
Bounds on the signed domination number of a graph
Let G = (V, E) be a simple graph on vertex set V and define a function f : V {-1, 1}. The function f is a signed dominating function if for every vertex x V, the closed neighbor...
Ruth Haas, Thomas B. Wexler
120views more  COMBINATORICS 2000»
8 years 11 months ago
The Characteristic Polynomial of a Graph is Reconstructible from the Characteristic Polynomials of its Vertex-Deleted Subgraphs
The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many...
Elias M. Hagos
93views more  COMBINATORICS 2004»
8 years 12 months ago
Degree Powers in Graphs with Forbidden Subgraphs
For every real p > 0 and simple graph G, set f (p, G) = uV (G) dp (u) , and let (r, p, n) be the maximum of f (p, G) taken over all Kr+1-free graphs G of order n. We prove tha...
Béla Bollobás, Vladimir Nikiforov
70views more  ARSCOM 2002»
8 years 12 months ago
On the Number of Graphical Forest Partitions
A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. ...
Deborah A. Frank, Carla D. Savage, James A. Seller...
99views more  JGT 2007»
8 years 12 months ago
The upper bound of the number of cycles in a 2-factor of a line graph
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
146views more  JCT 2007»
8 years 12 months ago
Laplacian spectral bounds for clique and independence numbers of graphs
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
Mei Lu, Huiqing Liu, Feng Tian
61views more  JGT 2008»
8 years 12 months ago
Irregularity strength of dense graphs
Let G be a simple graph of order n with no isolated vertices and no isolated edges. For a positive integer w, an assignment f on G is a function f : E(G) {1, 2, . . . , w}. For a ...
Bill Cuckler, Felix Lazebnik
103views more  ALGORITHMICA 2006»
9 years 2 days ago
Recognizing Hole-Free 4-Map Graphs in Cubic Time
We present a cubic-time algorithm for the following problem: Given a simple graph, decide whether it is realized by adjacencies of countries in a map without holes, in which at mo...
Zhi-Zhong Chen, Michelangelo Grigni, Christos H. P...