Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Hajiabolhassan, Hossein"'
Learning expressive molecular representations is crucial to facilitate the accurate prediction of molecular properties. Despite the significant advancement of graph neural networks (GNNs) in molecular representation learning, they generally face limi
Externí odkaz:
http://arxiv.org/abs/2207.08597
In this work, we present a generalization of Gale's lemma. Using this generalization, we introduce two combinatorial sharp lower bounds for ${\rm conid}({\rm B}_0(G))+1$ and ${\rm conid}({\rm B}(G))+2$, two famous topological lower bounds for the chr
Externí odkaz:
http://arxiv.org/abs/1607.08780
Recently, Kupavskii~[{\it On random subgraphs of {K}neser and {S}chrijver graphs. J. Combin. Theory Ser. A, {\rm 2016}.}] investigated the chromatic number of random Kneser graphs $\KG_{n,k}(\rho)$ and proved that, in many cases, the chromatic number
Externí odkaz:
http://arxiv.org/abs/1607.07432
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind, respectively
Externí odkaz:
http://arxiv.org/abs/1606.02544
In view of Tucker's lemma (an equivalent combinatorial version of the Borsuk- Ulam theorem), the present authors (2013) introduced the kth altermatic number of a graph G as a tight lower bound for the chromatic number of G. In this note, we present a
Externí odkaz:
http://arxiv.org/abs/1510.06932
In an earlier paper, the present authors (2013) introduced the altermatic number of graphs and used Tucker's Lemma, an equivalent combinatorial version of the Borsuk-Ulam Theorem, to show that the altermatic number is a lower bound for the chromatic
Externí odkaz:
http://arxiv.org/abs/1507.08456
One of the most famous conjecture in graph theory is Hedetniemi's conjecture stating that the chromatic number of the categorical product of graphs is the minimum of their chromatic numbers. Using a suitable extension of the definition of the categor
Externí odkaz:
http://arxiv.org/abs/1410.3021
For a graph $G$, the tree graph ${\cal T}_{G,t}$ has all tree subgraphs of $G$ with $t$ vertices as vertex set and two tree subgraphs are neighbors if they are edge-disjoint. Also, the $r^{th}$ cut number of $G$ is the minimum number of edges between
Externí odkaz:
http://arxiv.org/abs/1407.8035
A $50$ years unsolved conjecture by Hedetniemi [{\it Homomorphisms of graphs and automata, \newblock {\em Thesis (Ph.D.)--University of Michigan}, 1966}] asserts that the chromatic number of the categorical product of two graphs $G$ and $H$ is $\min\
Externí odkaz:
http://arxiv.org/abs/1403.4404
A Kneser representation KG(H) for a graph G is a bijective assignment of hyperedges of a hypergraph H to the vertices of G such that two vertices of G are adjacent if and only if the corresponding hyperedges are disjoint. In this paper, we introduce
Externí odkaz:
http://arxiv.org/abs/1401.0138