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Weighted colouring of hexagonal graphs. ★★
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ p:V(G)\rightarrow \mathbb{N} $](/files/tex/6b14cbdc1cda96520fd87d9507b262f943ccf8ba.png)
![$$\chi(G,p) \leq \frac{9}{8}\omega(G,p) + c $$](/files/tex/9b4ccf7620c2a90a97c40177afd9201723864ba8.png)
Keywords:
Colouring the square of a planar graph ★★
Author(s): Wegner
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
- \item at most
![$ 7 $](/files/tex/daebc9d78b81a4cd1f0e6bae70785e92cf2ce1ea.png)
![$ \Delta =3 $](/files/tex/aced9ebeab44df5a1f3efd1bfb967dd0fe0883c4.png)
![$ \Delta+5 $](/files/tex/a7be33e67abdf15a956bdc393747bb7f75bbd905.png)
![$ 4\leq\Delta\leq 7 $](/files/tex/edab53b759e15d01350d22f54590e6ee9a99bca9.png)
![$ \left\lfloor\frac32\,\Delta\right\rfloor+1 $](/files/tex/d5aa6f60013e17601f35a898a36936e347bc9a8b.png)
![$ \Delta\ge8 $](/files/tex/0782472fc66f76ac853e14ef0f2ded9aaac96451.png)
Keywords:
List chromatic number and maximum degree of bipartite graphs ★★
Author(s): Alon
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ c \log \Delta $](/files/tex/84aaddf436e9bd784cec262225dc1b22798556fd.png)
Keywords:
Hamilton decomposition of prisms over 3-connected cubic planar graphs ★★
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
Keywords:
Turán's problem for hypergraphs ★★
Author(s): Turan
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ 3n $](/files/tex/f36625fb2086623f510fdcab4f53cd27a419800a.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ \frac12 n^2(5n-3) $](/files/tex/77fae1e209cf2ef781abf9d88573e4981aa00b15.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ 2n $](/files/tex/56259815f2fdf87e92dd22e0058206e8e20fb986.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ n^2(n-1) $](/files/tex/edaf55f28dcd60182c7c9d88572ea01709769bde.png)
Keywords:
4-connected graphs are not uniquely hamiltonian ★★
Author(s): Fleischner
![$ 4 $](/files/tex/1f1498726bb4b7754ca36de46c0ccdd09136d115.png)
Keywords:
Every prism over a 3-connected planar graph is hamiltonian. ★★
Author(s): Kaiser; Král; Rosenfeld; Ryjácek; Voss
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ 3 $](/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png)
![$ G\square K_2 $](/files/tex/eb7d7828977b0484fd118a68143d72f9c6e865f3.png)
Keywords:
Hoàng-Reed Conjecture ★★★
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ C_1, \ldots, C_k $](/files/tex/0df670e43d33838d6e04e86a590da56100880e60.png)
![$ C_j $](/files/tex/b1365660549601f059d1b19f13f120a8fd821c25.png)
![$ \cup_{i=1}^{j-1}C_i $](/files/tex/b45609a301fcc110ef904d9f320f045d3947da71.png)
![$ 2 \leq j \leq k $](/files/tex/f4a8b4068d7bbb76eee5a6457f5fa87ff65184f1.png)
Keywords:
Edge-disjoint Hamilton cycles in highly strongly connected tournaments. ★★
Author(s): Thomassen
![$ k\geq 2 $](/files/tex/13bc863dca3c6b96ebfd2de373f0fe820c58b62b.png)
![$ f(k) $](/files/tex/e055b3867e7cb3cc4b2f50739eedda7657999214.png)
![$ f(k) $](/files/tex/e055b3867e7cb3cc4b2f50739eedda7657999214.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
Keywords:
Hamilton cycle in small d-diregular graphs ★★
Author(s): Jackson
An directed graph is -diregular if every vertex has indegree and outdegree at least
.
![$ d >2 $](/files/tex/6b29cd29e21416ff46f4898a33bcc7355436ee8f.png)
![$ d $](/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png)
![$ 4d+1 $](/files/tex/5d467147b18bddde059e7178ebf5bcf6c4b4f516.png)
Keywords:
Switching reconstruction of digraphs ★★
Keywords:
Switching reconstruction conjecture ★★
Author(s): Stanley
Keywords: reconstruction
Every 4-connected toroidal graph has a Hamilton cycle ★★
Author(s): Grunbaum; Nash-Williams
Keywords:
Acyclic list colouring of planar graphs. ★★★
Author(s): Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena
Keywords:
Earth-Moon Problem ★★
Author(s): Ringel
Keywords:
Triangle-packing vs triangle edge-transversal. ★★
Author(s): Tuza
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ 2k $](/files/tex/bded1a5bf39ed2baaf98bd8c04cea4667dd89b58.png)
Keywords:
Odd-cycle transversal in triangle-free graphs ★★
Author(s): Erdos; Faudree; Pach; Spencer
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ n^2/25 $](/files/tex/0db5eaf8ff84c2da58a206455442346f6fa11c19.png)
Keywords:
Simultaneous partition of hypergraphs ★★
![$ H_1 $](/files/tex/eb41970b0531bb084fea9f6967da01b53f441664.png)
![$ H_2 $](/files/tex/2d70749ca9db234020c5071434ce58006623b919.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ V $](/files/tex/517af4139f21bb21424f7896561555919bc4678a.png)
![$ V $](/files/tex/517af4139f21bb21424f7896561555919bc4678a.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ V_1, \dots , V_r $](/files/tex/9840205fdc1959213e766b6ed6ddd1dd952dc228.png)
![$ i=1,2 $](/files/tex/1db9f0079a9ca23741381d2fbc830c48d730c458.png)
![$ r!m_i/r^r -o(m_i) $](/files/tex/d65114aa913d6d3c960fc0fff99b77050111639d.png)
![$ H_i $](/files/tex/b5eebbb6562e3e98766f53decb43a78b1f076151.png)
![$ V_1, \dots , V_r $](/files/tex/9840205fdc1959213e766b6ed6ddd1dd952dc228.png)
Keywords:
Complexity of the H-factor problem. ★★
An -factor in a graph
is a set of vertex-disjoint copies of
covering all vertices of
.
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ cn $](/files/tex/d86cd3be7381a5c384b9e02ce96029e79af296a1.png)
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
Keywords:
Subgraph of large average degree and large girth. ★★
Author(s): Thomassen
![$ g $](/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ d $](/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png)
![$ d $](/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ g $](/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png)
Keywords: