Results 71 to 80 of about 1,022,735 (236)

Some results about ID-path-factor critical graphs [PDF]

Discrete Mathematics Letters, 2023
Zhiren Sun, Sizhong Zhou
doaj   +1 more source

Characterizing 2-crossing-critical graphs [PDF]

, 2013
It is very well-known that there are precisely two minimal non-planar graphs: $K_5$ and $K_{3,3}$ (degree 2 vertices being irrelevant in this context).
Bokal, Drago, Oporowski, Bogdan, Richter, R. Bruce, Salazar, Gelasio   +3 more
core  

On i−-ER-critical graphs

Discrete Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cockayne, E.J., Favaron, O., Mynhardt, C.M.   +2 more
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Ising Ferromagnets on Proximity Graphs with Varying Disorder of the Node Placement

Scientific Reports, 2017
We perform Monte Carlo simulations to determine the critical temperatures of Ising Ferromagnets (IFM) on different types of two-dimensional proximity graphs, in which the distribution of their underlying node sets has been changed systematically by means
Hendrik Schawe, Christoph Norrenbrock, Alexander K. Hartmann   +2 more
doaj   +1 more source

Critically (k, k)-connected graphs

Discrete Mathematics, 1987
A graph G, with vertex connectivity \(\kappa(G)\), minimum degree \(\delta(G)\), and complement \(\bar G,\) is critically \((k,k)\)-connected if \(\kappa(G)=\kappa(\bar G)=k\), and for each vertex v of G, either \(\kappa(G-v)=k-1\) or \(\kappa(\bar G-v)=k-1\). Theorem: If G is a critically \((k,k)\)-connected graph with \(k\geq 2\), \(\delta(G)\geq (3k-
Ando, Kiyoshi, Usami, Yoko
openaire   +1 more source

Planar 4-critical graphs with four triangles

, 2013
By the Grunbaum-Aksenov Theorem (extending Grotzsch's Theorem) every planar graph with at most three triangles is 3-colorable. However, there are infinitely many planar 4-critical graphs with exactly four triangles. We describe all such graphs.
Borodin, Oleg V., Dvořák, Zdeněk, Kostochka, Alexandr V., Lidický, Bernard, Yancey, Matthew   +4 more
core   +1 more source

Minimum $k$-critical-bipartite graphs: the irregular Case [PDF]

, 2023
Sylwia Cichacz, Agieszka Görlich, Karol Suchan   +2 more
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Clique-Critical Graphs

Electronic Notes in Discrete Mathematics, 2004
Abstract The clique graph of G, K(G), is the intersection graph of the family of cliques (maximal completes) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We present a new characterization of clique-critical graphs, and show the only way of adding vertices to a graph without changing its ...
openaire   +1 more source

3-Factor-criticality of vertex-transitive graphs [PDF]

, 2012
A graph of order $n$ is $p$-factor-critical, where $p$ is an integer of the same parity as $n$, if the removal of any set of $p$ vertices results in a graph with a perfect matching.
Sun, Wuyang, Zhang, Heping
core  

A Potts/Ising Correspondence on Thin Graphs

, 1998
We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the planar diagram
Ambjørn J, Bachas C, Baillie C, Baillie C, Banks T, Banks T, Baxter R, Baxter R, Baxter R, Baxter R, Boulatov D V, Brezin E, Brezin E, Brezin E, Callan C, Coleman S, D A Johnston, Essam J, Johnston D, Johnston D, Johnston D, Kazakov V, Kazakov V, Lipatov N, Lipatov N, Lipatov N, Lipatov N, Mehta M L, Parisi G, Peruggi F, Peruggi F, Peruggi F, Peruggi F, Whittle P, Whittle P, Whittle P   +35 more
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